|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre cosh $eq_no = 1 > array_tmp4_g[1] := sinh(array_tmp3[1]); > array_tmp4[1] := cosh(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre cosh $eq_no = 1 > array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1); > array_tmp4[2] := att(1,array_tmp4_g,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre cosh $eq_no = 1 > array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1); > array_tmp4[3] := att(2,array_tmp4_g,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre cosh $eq_no = 1 > array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1); > array_tmp4[4] := att(3,array_tmp4_g,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre cosh $eq_no = 1 > array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1); > array_tmp4[5] := att(4,array_tmp4_g,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit cosh $eq_no = 1 > array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1); > array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_g[1] := sinh(array_tmp3[1]); array_tmp4[1] := cosh(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1); array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1); array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1); array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1); array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1); array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2))); > end; exact_soln_y := proc(x) return 20.0*sqrt(0.1*x + 0.2)*sinh(sqrt(0.1*x + 0.2)) - 20.0*cosh(sqrt(0.1*x + 0.2)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > 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/cosh_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -1.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_g:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T00:09:28-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cosh_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"cosh_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"cosh_sqrt maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, 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/cosh_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -1.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0\ .1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_g := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := -1.0; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T00:09:28-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cosh_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "cosh_sqrt diffeq.mxt"); logitem_str(html_log_file, "cosh_sqrt maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostode.ode################# diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 6 estimated_steps = 6000000 step_error = 1.6666666666666666666666666666667e-17 est_needed_step_err = 1.6666666666666666666666666666667e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.9230751424511675824175824175824e-193 estimated_step_error = 2.9230751424511675824175824175824e-193 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7999928490042378917378917378917e-185 estimated_step_error = 2.7999928490042378917378917378917e-185 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 = 3.1999940740896825396825396825397e-177 estimated_step_error = 3.1999940740896825396825396825397e-177 best_h = 8.000e-06 opt_iter = 4 bytes used=4000512, 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 = 2.0553837607289987789987789987789e-169 estimated_step_error = 2.0553837607289987789987789987789e-169 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 = 1.5015197721744810744810744810745e-161 estimated_step_error = 1.5015197721744810744810744810745e-161 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.5785207980276760276760276760277e-154 estimated_step_error = 4.5785207980276760276760276760277e-154 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.9227851954708994708994708994709e-146 estimated_step_error = 4.9227851954708994708994708994709e-146 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1266716947106227106227106227106e-138 estimated_step_error = 2.1266716947106227106227106227106e-138 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 = 8.6609505035409035409035409035409e-131 estimated_step_error = 8.6609505035409035409035409035409e-131 best_h = 0.000512 opt_iter = 10 bytes used=8001644, alloc=3996964, time=0.25 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.4341843959299959299959299959300e-122 estimated_step_error = 2.4341843959299959299959299959300e-122 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 = 5.2063515715099715099715099715100e-115 estimated_step_error = 5.2063515715099715099715099715100e-115 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.8176933613349613349613349613350e-107 estimated_step_error = 3.8176933613349613349613349613350e-107 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.6380042940170940170940170940172e-99 estimated_step_error = 2.6380042940170940170940170940172e-99 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3580532643060643060643060643060e-91 estimated_step_error = 1.3580532643060643060643060643060e-91 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.8546723060643060643060643060643e-84 estimated_step_error = 4.8546723060643060643060643060643e-84 best_h = 0.032768 opt_iter = 16 bytes used=12002508, alloc=4193536, time=0.38 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5735845092389092389092389092390e-75 estimated_step_error = 1.5735845092389092389092389092390e-75 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 = 8.4987415547415547415547415547416e-68 estimated_step_error = 8.4987415547415547415547415547416e-68 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 = 1.5767116060236060236060236060236e-59 estimated_step_error = 1.5767116060236060236060236060236e-59 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = -18.974860763392397555820586777095 y[1] (numeric) = -18.974860763392397555820586777095 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = -18.964354040796229869016125972141 y[1] (numeric) = -18.964354040796229869016125972142 absolute error = 1e-30 relative error = 5.2730506815512625573464059010359e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00537 Order of pole (three term test) = -0.7228 Radius of convergence (six term test) for eq 1 = 0.2886 Order of pole (six term test) = -12.9 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = -18.953842233607323295055774089317 y[1] (numeric) = -18.953842233607323295055774089319 absolute error = 2e-30 relative error = 1.0551950234416175369373711118540e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01056 Order of pole (three term test) = -2.708 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=16003660, alloc=4324584, time=0.51 x[1] = -0.97 y[1] (analytic) = -18.943325340983855447367567229042 y[1] (numeric) = -18.943325340983855447367567229044 absolute error = 2e-30 relative error = 1.0557808431199790747124488584556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = -18.93280336208391999718039639065 y[1] (numeric) = -18.932803362083919997180396390651 absolute error = 1e-30 relative error = 5.2818379870921065857851759094252e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6695 Order of pole (six term test) = -13.38 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = -18.922276296065526667537651949257 y[1] (numeric) = -18.922276296065526667537651949258 absolute error = 1e-30 relative error = 5.2847764420812739099150571467851e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01473 Order of pole (three term test) = 1.778 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = -18.911744142086601227310535893506 y[1] (numeric) = -18.911744142086601227310535893507 absolute error = 1e-30 relative error = 5.2877195909951982785103105986264e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = -18.901206899304985485211041809093 y[1] (numeric) = -18.901206899304985485211041809094 absolute error = 1e-30 relative error = 5.2906674442930462110705252901870e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02007 Order of pole (three term test) = -29.08 Radius of convergence (six term test) for eq 1 = 0.01656 Order of pole (six term test) = -11.51 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = -18.890664566878437283804602592996 y[1] (numeric) = -18.890664566878437283804602592997 absolute error = 1e-30 relative error = 5.2936200124654675854327563488304e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03402 Order of pole (three term test) = -9.422 Radius of convergence (six term test) for eq 1 = 0.6727 Order of pole (six term test) = -9.998 TOP MAIN SOLVE Loop bytes used=20004560, alloc=4324584, time=0.64 x[1] = -0.91 y[1] (analytic) = -18.880117143964630493522405883301 y[1] (numeric) = -18.880117143964630493522405883303 absolute error = 2e-30 relative error = 1.0593154612069427880805618460195e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02913 Order of pole (three term test) = -37.07 Radius of convergence (six term test) for eq 1 = 0.1457 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = -18.869564629721155006673377189548 y[1] (numeric) = -18.869564629721155006673377189548 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1664 Order of pole (six term test) = -11.67 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = -18.859007023305516731455830708474 y[1] (numeric) = -18.859007023305516731455830708474 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.05497 Order of pole (six term test) = -11.52 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = -18.848444323875137585968787810106 y[1] (numeric) = -18.848444323875137585968787810107 absolute error = 1e-30 relative error = 5.3054776448224425222501010237981e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6774 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03566 Order of pole (three term test) = -16.67 Radius of convergence (six term test) for eq 1 = 0.1943 Order of pole (six term test) = -11.82 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = -18.837876530587355492222963179063 y[1] (numeric) = -18.837876530587355492222963179064 absolute error = 1e-30 relative error = 5.3084539458377079839422624088760e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = -18.827303642599424370151418595992 y[1] (numeric) = -18.827303642599424370151418595994 absolute error = 2e-30 relative error = 1.0622870050678518334519972948037e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005029 Order of pole (three term test) = -26.31 NO COMPLEX POLE (six term test) for Equation 1 bytes used=24009796, alloc=4390108, time=0.78 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = -18.816725659068514131619884344055 y[1] (numeric) = -18.816725659068514131619884344055 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = -18.806142579151710674436748225331 y[1] (numeric) = -18.806142579151710674436748225331 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1998 Order of pole (six term test) = -11.38 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = -18.795554402006015876362712172093 y[1] (numeric) = -18.795554402006015876362712172093 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6517 Order of pole (six term test) = 2.69 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = -18.784961126788347589120116437807 y[1] (numeric) = -18.784961126788347589120116437806 absolute error = 1e-30 relative error = 5.3234073429832502414758965670331e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5688 Order of pole (six term test) = -13.51 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = -18.774362752655539632401931352784 y[1] (numeric) = -18.774362752655539632401931352784 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1467 Order of pole (six term test) = -12.46 TOP MAIN SOLVE Loop bytes used=28010924, alloc=4390108, time=0.92 x[1] = -0.8 y[1] (analytic) = -18.763759278764341787880416629394 y[1] (numeric) = -18.763759278764341787880416629393 absolute error = 1e-30 relative error = 5.3294224528436470444695848561762e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.494 Order of pole (six term test) = -1.94 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = -18.753150704271419793215448201704 y[1] (numeric) = -18.753150704271419793215448201705 absolute error = 1e-30 relative error = 5.3324372835772562655750475955565e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001448 Order of pole (three term test) = -24.42 Radius of convergence (six term test) for eq 1 = 0.213 Order of pole (six term test) = -11.43 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = -18.742537028333355336062512584502 y[1] (numeric) = -18.742537028333355336062512584501 absolute error = 1e-30 relative error = 5.3354569794275236869803269596291e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003546 Order of pole (three term test) = -0.5806 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = -18.731918250106646048080368736524 y[1] (numeric) = -18.731918250106646048080368736524 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08617 Order of pole (three term test) = -11.39 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = -18.721294368747705498938377412881 y[1] (numeric) = -18.72129436874770549893837741288 absolute error = 1e-30 relative error = 5.3415110104210783191541914631597e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1291 Order of pole (three term test) = -60.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = -18.710665383412863190323497991485 y[1] (numeric) = -18.710665383412863190323497991485 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01584 Order of pole (three term test) = -27.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32011708, alloc=4455632, time=1.05 x[1] = -0.74 y[1] (analytic) = -18.700031293258364549946952758457 y[1] (numeric) = -18.700031293258364549946952758456 absolute error = 1e-30 relative error = 5.3475846340455839847198897747884e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3203 Order of pole (six term test) = -14.43 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = -18.689392097440370925550558637347 y[1] (numeric) = -18.689392097440370925550558637345 absolute error = 2e-30 relative error = 1.0701257641621808030485348967762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5903 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.164 Order of pole (six term test) = -11.93 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = -18.678747795114959578912726347113 y[1] (numeric) = -18.678747795114959578912726347111 absolute error = 2e-30 relative error = 1.0707355878122936392320526108498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4841 Order of pole (six term test) = -12.19 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = -18.668098385438123679854126973725 y[1] (numeric) = -18.668098385438123679854126973725 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02615 Order of pole (three term test) = -34.36 Radius of convergence (six term test) for eq 1 = 0.7819 Order of pole (six term test) = -22.11 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = -18.657443867565772300243025940306 y[1] (numeric) = -18.657443867565772300243025940304 absolute error = 2e-30 relative error = 1.0719582029544859807536710527631e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.69 y[1] (analytic) = -18.646784240653730408000284360674 y[1] (numeric) = -18.646784240653730408000284360673 absolute error = 1e-30 relative error = 5.3628549946955432040903648982398e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3949 Order of pole (six term test) = -10.93 TOP MAIN SOLVE Loop bytes used=36012400, alloc=4455632, time=1.19 x[1] = -0.68 y[1] (analytic) = -18.636119503857738861104027761244 y[1] (numeric) = -18.636119503857738861104027761243 absolute error = 1e-30 relative error = 5.3659239510295942590615105365752e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3028 Order of pole (six term test) = -12.41 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = -18.625449656333454401593982156101 y[1] (numeric) = -18.6254496563334544015939821561 absolute error = 1e-30 relative error = 5.3689978950921969633726131221611e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2387 Order of pole (six term test) = -11.16 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = -18.614774697236449649575477460205 y[1] (numeric) = -18.614774697236449649575477460204 absolute error = 1e-30 relative error = 5.3720768382357055779360974611067e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = -18.604094625722213097223118225584 y[1] (numeric) = -18.604094625722213097223118225583 absolute error = 1e-30 relative error = 5.3751607918473478779377933958306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005293 Order of pole (three term test) = -30.36 Radius of convergence (six term test) for eq 1 = 0.668 Order of pole (six term test) = -9.502 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (analytic) = -18.59340944094614910278412168542 y[1] (numeric) = -18.593409440946149102784121685418 absolute error = 2e-30 relative error = 1.0756499534698717827844863816556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07014 Order of pole (three term test) = 10.64 Radius of convergence (six term test) for eq 1 = 0.7399 Order of pole (six term test) = -15.43 TOP MAIN SOLVE Loop bytes used=40013416, alloc=4455632, time=1.33 x[1] = -0.63 y[1] (analytic) = -18.58271914206357788458132309091 y[1] (numeric) = -18.582719142063577884581323090909 absolute error = 1e-30 relative error = 5.3813437761991153892081135175160e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01642 Order of pole (three term test) = -19.31 Radius of convergence (six term test) for eq 1 = 0.1577 Order of pole (six term test) = -11.67 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = -18.572023728229735515015848325814 y[1] (numeric) = -18.572023728229735515015848325813 absolute error = 1e-30 relative error = 5.3844428298892706569452858394688e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05705 Order of pole (three term test) = -27.7 Radius of convergence (six term test) for eq 1 = 0.2046 Order of pole (six term test) = -10.82 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = -18.56132319859977391456945378355 y[1] (numeric) = -18.561323198599773914569453783548 absolute error = 2e-30 relative error = 1.0775093879895780680312333826066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = -18.550617552328760845806533491746 y[1] (numeric) = -18.550617552328760845806533491743 absolute error = 3e-30 relative error = 1.6171968353815765734333275837999e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05468 Order of pole (three term test) = -20.53 Radius of convergence (six term test) for eq 1 = 0.3119 Order of pole (six term test) = -11.74 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (analytic) = -18.539906788571679907375793469138 y[1] (numeric) = -18.539906788571679907375793469135 absolute error = 3e-30 relative error = 1.6181311126381994707256833754039e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06049 Order of pole (three term test) = -33.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = -18.529190906483430528011593299696 y[1] (numeric) = -18.529190906483430528011593299693 absolute error = 3e-30 relative error = 1.6190669172447725238688982281646e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03411 Order of pole (three term test) = -26.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44014268, alloc=4455632, time=1.47 x[1] = -0.57 y[1] (analytic) = -18.518469905218827960534954908861 y[1] (numeric) = -18.518469905218827960534954908859 absolute error = 2e-30 relative error = 1.0800028351350805179935529445446e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1049 Order of pole (three term test) = 20.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = -18.507743783932603275854238526798 y[1] (numeric) = -18.507743783932603275854238526795 absolute error = 3e-30 relative error = 1.6209431225238992241111042429010e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7059 Order of pole (six term test) = -14.67 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = -18.497012541779403356965485823526 y[1] (numeric) = -18.497012541779403356965485823523 absolute error = 3e-30 relative error = 1.6218835302316346378872485919896e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09573 Order of pole (three term test) = -23.46 Radius of convergence (six term test) for eq 1 = 0.3902 Order of pole (six term test) = -11.44 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = -18.486276177913790892952430200843 y[1] (numeric) = -18.48627617791379089295243020084 absolute error = 3e-30 relative error = 1.6228254793597675924253764536607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6708 Order of pole (six term test) = -12.72 TOP MAIN SOLVE Loop x[1] = -0.53 y[1] (analytic) = -18.475534691490244372986174225901 y[1] (numeric) = -18.475534691490244372986174225899 absolute error = 2e-30 relative error = 1.0825126489687964541494898087285e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4843 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = -18.464788081663158080324534191337 y[1] (numeric) = -18.464788081663158080324534191335 absolute error = 2e-30 relative error = 1.0831426773785406208666073201362e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5304 Order of pole (six term test) = -12.68 TOP MAIN SOLVE Loop bytes used=48015528, alloc=4455632, time=1.61 x[1] = -0.51 y[1] (analytic) = -18.454036347586842086311051786829 y[1] (numeric) = -18.454036347586842086311051786828 absolute error = 1e-30 relative error = 5.4188687025685080485302370465938e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004249 Order of pole (three term test) = -24.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (analytic) = -18.443279488415522244373672866982 y[1] (numeric) = -18.44327948841552224437367286698 absolute error = 2e-30 relative error = 1.0844058407596260383274651855921e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06227 Order of pole (three term test) = -29.53 Radius of convergence (six term test) for eq 1 = 0.05808 Order of pole (six term test) = -11.78 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (analytic) = -18.432517503303340184023093300395 y[1] (numeric) = -18.432517503303340184023093300393 absolute error = 2e-30 relative error = 1.0850389805090784335049681250908e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1205 Order of pole (six term test) = -11.61 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (analytic) = -18.421750391404353304850771884829 y[1] (numeric) = -18.421750391404353304850771884828 absolute error = 1e-30 relative error = 5.4283658108113501875349284021554e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01143 Order of pole (three term test) = -24.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (analytic) = -18.410978151872534770526610313331 y[1] (numeric) = -18.41097815187253477052661031333 absolute error = 1e-30 relative error = 5.4315419406344387442873822317072e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 bytes used=52016620, alloc=4455632, time=1.74 y[1] (analytic) = -18.400200783861773502796300176202 y[1] (numeric) = -18.4002007838617735027963001762 absolute error = 2e-30 relative error = 1.0869446608181231982103762656251e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5651 Order of pole (six term test) = -9.747 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = -18.389418286525874175478336983693 y[1] (numeric) = -18.389418286525874175478336983691 absolute error = 2e-30 relative error = 1.0875819826587019600737499976334e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3831 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (analytic) = -18.378630659018557208460701194317 y[1] (numeric) = -18.378630659018557208460701194315 absolute error = 2e-30 relative error = 1.0882203560789129011247009864161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = -18.367837900493458761697206233636 y[1] (numeric) = -18.367837900493458761697206233635 absolute error = 1e-30 relative error = 5.4442989175831883293035790363478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004935 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (analytic) = -18.357040010104130729203513488424 y[1] (numeric) = -18.357040010104130729203513488423 absolute error = 1e-30 relative error = 5.4475013370869015016888894502101e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4926 Order of pole (three term test) = -128.8 Radius of convergence (six term test) for eq 1 = 0.3998 Order of pole (six term test) = -11.96 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = -18.346236987004040733052814261068 y[1] (numeric) = -18.346236987004040733052814261066 absolute error = 2e-30 relative error = 1.0901418102342970147502723689827e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0197 Order of pole (three term test) = -2.269 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=56017904, alloc=4455632, time=1.88 x[1] = -0.4 y[1] (analytic) = -18.335428830346572117371178669092 y[1] (numeric) = -18.335428830346572117371178669092 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = -18.324615539285023942332571474698 y[1] (numeric) = -18.324615539285023942332571474696 absolute error = 2e-30 relative error = 1.0914280824677178983057829549571e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05764 Order of pole (three term test) = -42.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = -18.313797112972610978153534829146 y[1] (numeric) = -18.313797112972610978153534829146 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (analytic) = -18.302973550562463699087537916942 y[1] (numeric) = -18.302973550562463699087537916942 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3471 Order of pole (six term test) = -11.24 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = -18.292144851207628277418993484604 y[1] (numeric) = -18.292144851207628277418993484603 absolute error = 1e-30 relative error = 5.4668274723069506284098295288285e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0306 Order of pole (three term test) = -26.01 Radius of convergence (six term test) for eq 1 = 0.1539 Order of pole (six term test) = -11.51 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = -18.281311014061066577456941238958 y[1] (numeric) = -18.281311014061066577456941238957 absolute error = 1e-30 relative error = 5.4700672136196917565774759678215e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01531 Order of pole (three term test) = -22.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=60019440, alloc=4521156, time=2.01 x[1] = -0.34 y[1] (analytic) = -18.270472038275656149528398099814 y[1] (numeric) = -18.270472038275656149528398099814 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.401 Order of pole (six term test) = -12.72 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = -18.259627923004190223971375291892 y[1] (numeric) = -18.259627923004190223971375291891 absolute error = 1e-30 relative error = 5.4765628533983491715561693249545e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -20.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = -18.248778667399377705127562260858 y[1] (numeric) = -18.248778667399377705127562260858 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.31 y[1] (analytic) = -18.23792427061384316533467739839 y[1] (numeric) = -18.23792427061384316533467739839 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = -18.22706473180012683891848556109 y[1] (numeric) = -18.227064731800126838918485561088 absolute error = 2e-30 relative error = 1.0972693790408663315952966243978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01433 Order of pole (three term test) = -27.43 Radius of convergence (six term test) for eq 1 = 0.3679 Order of pole (six term test) = -12.41 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = -18.21620005011068461618448236814 y[1] (numeric) = -18.216200050110684616184482368139 absolute error = 1e-30 relative error = 5.4896191151234301258809224270333e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06662 Order of pole (three term test) = -7.164 Radius of convergence (six term test) for eq 1 = 0.4178 Order of pole (six term test) = -12.48 TOP MAIN SOLVE Loop bytes used=64020232, alloc=4521156, time=2.15 x[1] = -0.28 y[1] (analytic) = -18.205330224697888037409245262597 y[1] (numeric) = -18.205330224697888037409245262596 absolute error = 1e-30 relative error = 5.4928967926292844726649112498043e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3502 Order of pole (six term test) = -12.39 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (analytic) = -18.19445525471402428683145132114 y[1] (numeric) = -18.194455254714024286831451321139 absolute error = 1e-30 relative error = 5.4961799405393505406270220450833e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01094 Order of pole (three term test) = -27.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (analytic) = -18.18357513931129618664256179719 y[1] (numeric) = -18.183575139311296186642561797189 absolute error = 1e-30 relative error = 5.4994685717116631320928017733220e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04141 Order of pole (three term test) = -29.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (analytic) = -18.172689877641822190977173382252 y[1] (numeric) = -18.17268987764182219097717338225 absolute error = 2e-30 relative error = 1.1005525398089992925715019752693e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2844 Order of pole (six term test) = -11.81 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = -18.161799468857636379903036170341 y[1] (numeric) = -18.161799468857636379903036170339 absolute error = 2e-30 relative error = 1.1012124670958050755533131404518e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4584 Order of pole (six term test) = -11.55 TOP MAIN SOLVE Loop bytes used=68021532, alloc=4521156, time=2.29 x[1] = -0.23 y[1] (analytic) = -18.15090391211068845341073831038 y[1] (numeric) = -18.150903912110688453410738310379 absolute error = 1e-30 relative error = 5.5093674939944873326603038826595e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = -18.140003206552843725403057331419 y[1] (numeric) = -18.140003206552843725403057331419 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07137 Order of pole (three term test) = -24.23 Radius of convergence (six term test) for eq 1 = 0.3278 Order of pole (six term test) = -11.21 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (analytic) = -18.129097351335883117683978125549 y[1] (numeric) = -18.129097351335883117683978125548 absolute error = 1e-30 relative error = 5.5159944293989505310106944733101e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2745 Order of pole (six term test) = -12.36 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (analytic) = -18.118186345611503153947377573373 y[1] (numeric) = -18.118186345611503153947377573373 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5261 Order of pole (six term test) = -11.63 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = -18.107270188531315953765375796921 y[1] (numeric) = -18.107270188531315953765375796922 absolute error = 1e-30 relative error = 5.5226436099317419288448990872297e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02276 Order of pole (three term test) = -0.3181 Radius of convergence (six term test) for eq 1 = 0.1843 Order of pole (six term test) = -12.53 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = -18.096348879246849226576354024841 y[1] (numeric) = -18.09634887924684922657635402484 absolute error = 1e-30 relative error = 5.5259765750140585005892519231986e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2463 Order of pole (six term test) = -11.1 TOP MAIN SOLVE Loop bytes used=72022508, alloc=4521156, time=2.42 x[1] = -0.17 y[1] (analytic) = -18.085422416909546265672639054744 y[1] (numeric) = -18.085422416909546265672639054744 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04096 Order of pole (three term test) = -17.03 Radius of convergence (six term test) for eq 1 = 0.3698 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (analytic) = -18.074490800670765942187854297595 y[1] (numeric) = -18.074490800670765942187854297594 absolute error = 1e-30 relative error = 5.5326593209634918488419883569738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.111 Order of pole (three term test) = 45.86 Radius of convergence (six term test) for eq 1 = 1.359 Order of pole (six term test) = -12.36 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (analytic) = -18.063554029681782699083937388954 y[1] (numeric) = -18.063554029681782699083937388955 absolute error = 1e-30 relative error = 5.5360091284185482009872248077967e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4264 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = -18.052612103093786545137824352002 y[1] (numeric) = -18.052612103093786545137824352002 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1295 Order of pole (three term test) = -63.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = -18.041665020057883048927800297136 y[1] (numeric) = -18.041665020057883048927800297136 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = -18.030712779725093332819516643072 y[1] (numeric) = -18.030712779725093332819516643072 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2329 Order of pole (six term test) = -12.23 TOP MAIN SOLVE Loop bytes used=76023424, alloc=4521156, time=2.56 x[1] = -0.11 y[1] (analytic) = -18.019755381246354066951674844261 y[1] (numeric) = -18.019755381246354066951674844262 absolute error = 1e-30 relative error = 5.5494649002878640549070899718284e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4186 Order of pole (six term test) = -12.15 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = -18.008792823772517463221376609506 y[1] (numeric) = -18.008792823772517463221376609507 absolute error = 1e-30 relative error = 5.5528430460921812436115228063383e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09 y[1] (analytic) = -17.997825106454351269269140596623 y[1] (numeric) = -17.997825106454351269269140596623 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2959 Order of pole (three term test) = 12.01 Radius of convergence (six term test) for eq 1 = 0.3018 Order of pole (six term test) = -12.51 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = -17.986852228442538762463585568025 y[1] (numeric) = -17.986852228442538762463585568025 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006806 Order of pole (three term test) = -2.147 Radius of convergence (six term test) for eq 1 = 0.313 Order of pole (six term test) = -11.33 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = -17.975874188887678743885779992075 y[1] (numeric) = -17.975874188887678743885779992074 absolute error = 1e-30 relative error = 5.5630117873109044194439746085453e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5284 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop bytes used=80024248, alloc=4521156, time=2.70 x[1] = -0.06 y[1] (analytic) = -17.964890986940285532313258075063 y[1] (numeric) = -17.964890986940285532313258075063 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2739 Order of pole (three term test) = -71.33 Radius of convergence (six term test) for eq 1 = 0.3814 Order of pole (six term test) = -11.9 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (analytic) = -17.953902621750788958203702208685 y[1] (numeric) = -17.953902621750788958203702208684 absolute error = 1e-30 relative error = 5.5698196713427657668908149671761e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (analytic) = -17.942909092469534357678291817842 y[1] (numeric) = -17.942909092469534357678291817841 absolute error = 1e-30 relative error = 5.5732322715701120136498543781684e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2419 Order of pole (three term test) = -39.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = -17.931910398246782566504718593666 y[1] (numeric) = -17.931910398246782566504718593666 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (analytic) = -17.920906538232709914079868096589 y[1] (numeric) = -17.920906538232709914079868096589 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01783 Order of pole (three term test) = -29.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (analytic) = -17.909897511577408217412167714326 y[1] (numeric) = -17.909897511577408217412167714325 absolute error = 1e-30 relative error = 5.5835048712789944677960162367382e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02363 Order of pole (three term test) = -7.129 Radius of convergence (six term test) for eq 1 = 0.3494 Order of pole (six term test) = -11.56 TOP MAIN SOLVE Loop bytes used=84025328, alloc=4521156, time=2.83 x[1] = 0 y[1] (analytic) = -17.898883317430884775103600959624 y[1] (numeric) = -17.898883317430884775103600959623 absolute error = 1e-30 relative error = 5.5869407172800931168569624150308e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04472 Order of pole (three term test) = -6.967 Radius of convergence (six term test) for eq 1 = 0.3643 Order of pole (six term test) = -11.1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = -17.88786395494306236133138809264 y[1] (numeric) = -17.887863954943062361331388092639 absolute error = 1e-30 relative error = 5.5903824096541382251171225029173e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005578 Order of pole (three term test) = -25.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = -17.876839423263779219829333052785 y[1] (numeric) = -17.876839423263779219829333052784 absolute error = 1e-30 relative error = 5.5938299624634080876726491598148e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.14 Order of pole (three term test) = -43.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = -17.865809721542789057868836684899 y[1] (numeric) = -17.865809721542789057868836684899 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03703 Order of pole (three term test) = -27.55 Radius of convergence (six term test) for eq 1 = 0.1744 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = -17.854774848929761040239576244611 y[1] (numeric) = -17.85477484892976104023957624461 absolute error = 1e-30 relative error = 5.6007427058647078401781373297503e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008072 Order of pole (three term test) = -24.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = -17.84373480457427978322985116772 y[1] (numeric) = -17.843734804574279783229851167718 absolute error = 2e-30 relative error = 1.1208415849619641846338796550107e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1867 Order of pole (three term test) = -53.8 Radius of convergence (six term test) for eq 1 = 0.6529 Order of pole (six term test) = -9.572 TOP MAIN SOLVE Loop bytes used=88026152, alloc=4521156, time=2.97 x[1] = 0.06 y[1] (analytic) = -17.832689587625845348606595088469 y[1] (numeric) = -17.832689587625845348606595088468 absolute error = 1e-30 relative error = 5.6076790608966965888822659040002e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00583 Order of pole (three term test) = -24.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = -17.821639197233873237595054091557 y[1] (numeric) = -17.821639197233873237595054091556 absolute error = 1e-30 relative error = 5.6111561284172540725012259202474e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07727 Order of pole (three term test) = -16.78 Radius of convergence (six term test) for eq 1 = 0.8015 Order of pole (six term test) = -9.878 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = -17.81058363254769438485813118272 y[1] (numeric) = -17.810583632547694384858131182719 absolute error = 1e-30 relative error = 5.6146391417099011362190273037582e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2799 Order of pole (six term test) = -12.54 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = -17.799522892716555152475396962759 y[1] (numeric) = -17.799522892716555152475396962757 absolute error = 2e-30 relative error = 1.1236256230319445952463500464499e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = -17.788456976889617323921766489844 y[1] (numeric) = -17.788456976889617323921766489842 absolute error = 2e-30 relative error = 1.1243246126397344103672223289290e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01639 Order of pole (three term test) = -2.357 Radius of convergence (six term test) for eq 1 = 0.3001 Order of pole (six term test) = -11.55 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = -17.777385884215958098045842314954 y[1] (numeric) = -17.777385884215958098045842314952 bytes used=92027012, alloc=4521156, time=3.11 absolute error = 2e-30 relative error = 1.1250248000611517683768578108678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = -17.766309613844570083047923675291 y[1] (numeric) = -17.76630961384457008304792367529 absolute error = 1e-30 relative error = 5.6286309410072435338858011121747e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03637 Order of pole (three term test) = -18.54 Radius of convergence (six term test) for eq 1 = 0.2475 Order of pole (six term test) = -11.65 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = -17.755228164924361290457681830526 y[1] (numeric) = -17.755228164924361290457681830525 absolute error = 1e-30 relative error = 5.6321438998768286510804927495099e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02074 Order of pole (three term test) = -30.43 Radius of convergence (six term test) for eq 1 = 0.09875 Order of pole (six term test) = -11.4 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = -17.744141536604155129111501526709 y[1] (numeric) = -17.744141536604155129111501526708 absolute error = 1e-30 relative error = 5.6356628915358526228414355527883e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03298 Order of pole (three term test) = -26.76 Radius of convergence (six term test) for eq 1 = 0.4097 Order of pole (six term test) = -11.22 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = -17.733049728032690399129488572706 y[1] (numeric) = -17.733049728032690399129488572704 absolute error = 2e-30 relative error = 1.1278375861306968607603144806453e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03649 Order of pole (three term test) = -6.554 Radius of convergence (six term test) for eq 1 = 0.1761 Order of pole (six term test) = -11.83 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = -17.721952738358621285892143513994 y[1] (numeric) = -17.721952738358621285892143513992 absolute error = 2e-30 relative error = 1.1285438063893836894266422895711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08629 Order of pole (three term test) = 4.67 Radius of convergence (six term test) for eq 1 = 0.4092 Order of pole (six term test) = -12.23 TOP MAIN SOLVE Loop bytes used=96027852, alloc=4521156, time=3.25 x[1] = 0.17 y[1] (analytic) = -17.710850566730517354016701388671 y[1] (numeric) = -17.710850566730517354016701388669 absolute error = 2e-30 relative error = 1.1292512420363144274890020518407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.299 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03814 Order of pole (three term test) = -3.022 Radius of convergence (six term test) for eq 1 = 0.4895 Order of pole (six term test) = -12.24 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = -17.699743212296863541333137550514 y[1] (numeric) = -17.699743212296863541333137550513 absolute error = 1e-30 relative error = 5.6497994801712821887968887174386e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7357 Order of pole (six term test) = -11.39 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = -17.68863067420606015285983954394 y[1] (numeric) = -17.688630674206060152859839543938 absolute error = 2e-30 relative error = 1.1306697713557007026738741713971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01879 Order of pole (three term test) = -4.695 Radius of convergence (six term test) for eq 1 = 0.8626 Order of pole (six term test) = -9.641 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = -17.677512951606422854778945015693 y[1] (numeric) = -17.677512951606422854778945015692 absolute error = 1e-30 relative error = 5.6569043549145084663601838250640e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002153 Order of pole (three term test) = -25.06 Radius of convergence (six term test) for eq 1 = 0.3562 Order of pole (six term test) = -11.06 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = -17.666390043646182668411345648138 y[1] (numeric) = -17.666390043646182668411345648137 absolute error = 1e-30 relative error = 5.6604659895395871727175383873576e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = -17.655261949473485964191357098956 y[1] (numeric) = -17.655261949473485964191357098954 absolute error = 2e-30 relative error = 1.1328067551326497682712764582078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005884 Order of pole (three term test) = -1.095 Radius of convergence (six term test) for eq 1 = 0.3517 Order of pole (six term test) = -12.18 TOP MAIN SOLVE Loop bytes used=100028816, alloc=4521156, time=3.39 x[1] = 0.23 y[1] (analytic) = -17.644128668236394455641054932112 y[1] (numeric) = -17.644128668236394455641054932111 absolute error = 1e-30 relative error = 5.6676077283444240725410574823604e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = -17.632990199082885193344276524943 y[1] (numeric) = -17.632990199082885193344276524942 absolute error = 1e-30 relative error = 5.6711878626916681641552069199931e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5622 Order of pole (three term test) = -119.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = -17.621846541160850558920288936173 y[1] (numeric) = -17.621846541160850558920288936172 absolute error = 1e-30 relative error = 5.6747741938633654226174687915256e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.115 Order of pole (six term test) = -11.8 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = -17.610697693618098258997122719726 y[1] (numeric) = -17.610697693618098258997122719725 absolute error = 1e-30 relative error = 5.6783667370679344842394676147807e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.046 Order of pole (six term test) = -10.22 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = -17.599543655602351319184571669164 y[1] (numeric) = -17.599543655602351319184571669163 absolute error = 1e-30 relative error = 5.6819655075640346528608652945226e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2819 Order of pole (six term test) = -11.6 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = -17.588384426261248078046858477586 y[1] (numeric) = -17.588384426261248078046858477584 absolute error = 2e-30 relative error = 1.1371141041321546519269546072306e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06673 Order of pole (three term test) = -3.054 NO COMPLEX POLE (six term test) for Equation 1 bytes used=104031632, alloc=4586680, time=3.53 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = -17.577220004742342181074966297828 y[1] (numeric) = -17.577220004742342181074966297827 absolute error = 1e-30 relative error = 5.6891817917179140508756494398206e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1272 Order of pole (three term test) = -44.94 Radius of convergence (six term test) for eq 1 = 0.8157 Order of pole (six term test) = -10.59 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = -17.566050390193102574658636187812 y[1] (numeric) = -17.566050390193102574658636187811 absolute error = 1e-30 relative error = 5.6927993361460866099209234810159e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1707 Order of pole (three term test) = 13.24 Radius of convergence (six term test) for eq 1 = 0.7138 Order of pole (six term test) = -14.9 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = -17.554875581760913500058030425856 y[1] (numeric) = -17.554875581760913500058030425854 absolute error = 2e-30 relative error = 1.1392846338813993637993971637661e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4905 Order of pole (six term test) = -11.19 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = -17.543695578593074487375061680805 y[1] (numeric) = -17.543695578593074487375061680803 absolute error = 2e-30 relative error = 1.1400106614027276734239780747911e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.805 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = -17.532510379836800349524388021811 y[1] (numeric) = -17.53251037983680034952438802181 absolute error = 1e-30 relative error = 5.7036897645305053101011028206684e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7044 Order of pole (six term test) = -12.32 TOP MAIN SOLVE Loop bytes used=108032508, alloc=4586680, time=3.66 x[1] = 0.34 y[1] (analytic) = -17.521319984639221176204073752594 y[1] (numeric) = -17.521319984639221176204073752593 absolute error = 1e-30 relative error = 5.7073325575738056887689259980873e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = -17.510124392147382327865916055014 y[1] (numeric) = -17.510124392147382327865916055013 absolute error = 1e-30 relative error = 5.7109817018116762115568267459673e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1086 Order of pole (three term test) = -11.44 Radius of convergence (six term test) for eq 1 = 1.291 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = -17.498923601508244429685437426803 y[1] (numeric) = -17.498923601508244429685437426801 absolute error = 2e-30 relative error = 1.1429274425928796015301573624021e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03154 Order of pole (three term test) = -22.4 Radius of convergence (six term test) for eq 1 = 0.3529 Order of pole (six term test) = -10.94 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = -17.487717611868683365531543898272 y[1] (numeric) = -17.48771761186868336553154389827 absolute error = 2e-30 relative error = 1.1436598213609226913858009573505e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.926 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.001863 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = -17.476506422375490271935849012847 y[1] (numeric) = -17.476506422375490271935849012844 absolute error = 3e-30 relative error = 1.7165902197472632308906367141958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4855 Order of pole (six term test) = -12.27 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = -17.465290032175371532061663556235 y[1] (numeric) = -17.465290032175371532061663556233 absolute error = 2e-30 relative error = 1.1451284211802419310874612009775e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1891 Order of pole (three term test) = -74.22 Radius of convergence (six term test) for eq 1 = 0.1587 Order of pole (six term test) = -11.93 TOP MAIN SOLVE Loop bytes used=112033604, alloc=4586680, time=3.80 x[1] = 0.4 y[1] (analytic) = -17.454068440414948769672651019096 y[1] (numeric) = -17.454068440414948769672651019093 absolute error = 3e-30 relative error = 1.7187969728899944264674958444753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = -17.442841646240758843101148777995 y[1] (numeric) = -17.442841646240758843101148777993 absolute error = 2e-30 relative error = 1.1466021652676273679445690154192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = -17.431609648799253839216154979526 y[1] (numeric) = -17.431609648799253839216154979523 absolute error = 3e-30 relative error = 1.7210114616160245365063251700936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.16 Order of pole (three term test) = 60.26 Radius of convergence (six term test) for eq 1 = 0.4907 Order of pole (six term test) = -12.78 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = -17.420372447236801067390981112378 y[1] (numeric) = -17.420372447236801067390981112377 absolute error = 1e-30 relative error = 5.7404053962039073431827623716395e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02433 Order of pole (three term test) = -28.27 Radius of convergence (six term test) for eq 1 = 0.2178 Order of pole (six term test) = -11.57 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = -17.409130040699683053470570252235 y[1] (numeric) = -17.409130040699683053470570252233 absolute error = 2e-30 relative error = 1.1488224829869895312246183279082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01288 Order of pole (three term test) = -19.49 Radius of convergence (six term test) for eq 1 = 0.7481 Order of pole (six term test) = -11.38 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = -17.397882428334097533738480964264 y[1] (numeric) = -17.397882428334097533738480964262 absolute error = 2e-30 relative error = 1.1495651888892011258003948435669e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002972 Order of pole (three term test) = -25.58 NO COMPLEX POLE (six term test) for Equation 1 bytes used=116035392, alloc=4586680, time=3.94 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = -17.386629609286157448883536848099 y[1] (numeric) = -17.386629609286157448883536848096 absolute error = 3e-30 relative error = 1.7254638002972739166244488441520e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.488 Order of pole (six term test) = -14.15 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = -17.375371582701890937966141710078 y[1] (numeric) = -17.375371582701890937966141710076 absolute error = 2e-30 relative error = 1.1510545201756183808088972832204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5671 Order of pole (six term test) = -11.55 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = -17.364108347727241332384260347618 y[1] (numeric) = -17.364108347727241332384260347615 absolute error = 3e-30 relative error = 1.7277017281412350250445013011428e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08117 Order of pole (three term test) = -34.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = -17.3528399035080671498390649305 y[1] (numeric) = -17.352839903508067149839064930497 absolute error = 3e-30 relative error = 1.7288236488561835085900098642197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4822 Order of pole (six term test) = -11.64 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = -17.341566249190142088300246963939 y[1] (numeric) = -17.341566249190142088300246963937 absolute error = 2e-30 relative error = 1.1532983649002296897700828938851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.704 Order of pole (six term test) = -12.68 TOP MAIN SOLVE Loop bytes used=120037176, alloc=4586680, time=4.08 x[1] = 0.51 y[1] (analytic) = -17.330287383919155019970994818231 y[1] (numeric) = -17.330287383919155019970994818229 absolute error = 2e-30 relative error = 1.1540489523882957822569669929707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06783 Order of pole (three term test) = -17.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = -17.319003306840709985252636809814 y[1] (numeric) = -17.319003306840709985252636809812 absolute error = 2e-30 relative error = 1.1548008650186204532733555543499e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01791 Order of pole (three term test) = 0.1918 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = -17.307714017100326186708949818565 y[1] (numeric) = -17.307714017100326186708949818562 absolute error = 3e-30 relative error = 1.7333311591790499767012508185656e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = -17.296419513843437983030133426156 y[1] (numeric) = -17.296419513843437983030133426154 absolute error = 2e-30 relative error = 1.1563086790299409951643180076143e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1012 Order of pole (three term test) = -27.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = -17.285119796215394882996449560301 y[1] (numeric) = -17.285119796215394882996449560298 absolute error = 3e-30 relative error = 1.7355968806515618616406292681682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2726 Order of pole (three term test) = -16.12 Radius of convergence (six term test) for eq 1 = 0.3468 Order of pole (six term test) = -12.3 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = -17.273814863361461539441527629686 y[1] (numeric) = -17.273814863361461539441527629684 absolute error = 2e-30 relative error = 1.1578218336947039871486493371725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4548 Order of pole (six term test) = -12.67 TOP MAIN SOLVE Loop bytes used=124037876, alloc=4586680, time=4.21 x[1] = 0.57 y[1] (analytic) = -17.262504714426817743215335134456 y[1] (numeric) = -17.262504714426817743215335134453 absolute error = 3e-30 relative error = 1.7378706332765289333959342268418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = -17.251189348556558417146813737014 y[1] (numeric) = -17.251189348556558417146813737011 absolute error = 3e-30 relative error = 1.7390105339322682767781201068911e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2702 Order of pole (six term test) = -11.44 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = -17.239868764895693610006180778018 y[1] (numeric) = -17.239868764895693610006180778016 absolute error = 2e-30 relative error = 1.1601016384025244645722616301529e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004605 Order of pole (three term test) = -0.6797 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = -17.228542962589148490466896222348 y[1] (numeric) = -17.228542962589148490466896222346 absolute error = 2e-30 relative error = 1.1608642729352633555549790886971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = -17.217211940781763341067295019881 y[1] (numeric) = -17.217211940781763341067295019879 absolute error = 2e-30 relative error = 1.1616282629725171175455952846891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = -17.205875698618293552171884865895 y[1] (numeric) = -17.205875698618293552171884865894 absolute error = 1e-30 relative error = 5.8119680597268544572070606421822e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05885 Order of pole (three term test) = -25.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=128038680, alloc=4586680, time=4.35 x[1] = 0.63 y[1] (analytic) = -17.19453423524340961593230934592 y[1] (numeric) = -17.194534235243409615932309345917 absolute error = 3e-30 relative error = 1.7447404849448841955594858589911e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02044 Order of pole (three term test) = -23.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = -17.18318754980169712024797644983 y[1] (numeric) = -17.183187549801697120247976449827 absolute error = 3e-30 relative error = 1.7458926007210004252360455794416e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004615 Order of pole (three term test) = -24.78 Radius of convergence (six term test) for eq 1 = 0.3011 Order of pole (six term test) = -12.58 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = -17.171835641437656742726352440042 y[1] (numeric) = -17.17183564143765674272635244004 absolute error = 2e-30 relative error = 1.1646978469638767336276179999816e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01892 Order of pole (three term test) = -23.37 Radius of convergence (six term test) for eq 1 = 0.1941 Order of pole (six term test) = -11.57 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = -17.160478509295704244642921058588 y[1] (numeric) = -17.160478509295704244642921058585 absolute error = 3e-30 relative error = 1.7482029993364824855303640893384e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02114 Order of pole (three term test) = -25.31 Radius of convergence (six term test) for eq 1 = 0.6293 Order of pole (six term test) = -12.35 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = -17.149116152520170464900808057895 y[1] (numeric) = -17.149116152520170464900808057892 absolute error = 3e-30 relative error = 1.7493612926279767099179786829431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01121 Order of pole (three term test) = -20.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=132039468, alloc=4586680, time=4.49 x[1] = 0.68 y[1] (analytic) = -17.137748570255301313990071040103 y[1] (numeric) = -17.137748570255301313990071040101 absolute error = 2e-30 relative error = 1.1670144370487785538083701616975e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9383 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = -17.126375761645257767946654589717 y[1] (numeric) = -17.126375761645257767946654589715 absolute error = 2e-30 relative error = 1.1677893956285988568965229040478e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0276 Order of pole (three term test) = -26.24 Radius of convergence (six term test) for eq 1 = 0.3914 Order of pole (six term test) = -11.42 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = -17.114997725834115862311010684406 y[1] (numeric) = -17.114997725834115862311010684403 absolute error = 3e-30 relative error = 1.7528486115260597365283192230790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6798 Order of pole (six term test) = -12.96 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = -17.103614461965866686086384368771 y[1] (numeric) = -17.103614461965866686086384368768 absolute error = 3e-30 relative error = 1.7540152151296703119024783295129e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1443 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = -17.092225969184416375696764675903 y[1] (numeric) = -17.092225969184416375696764675901 absolute error = 2e-30 relative error = 1.1701226063859681604826931715820e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = -17.080832246633586108944500781519 y[1] (numeric) = -17.080832246633586108944500781517 absolute error = 2e-30 relative error = 1.1709031334782732599942061053824e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1097 Order of pole (three term test) = -35.69 Radius of convergence (six term test) for eq 1 = 0.1432 Order of pole (six term test) = -12.07 TOP MAIN SOLVE Loop bytes used=136040472, alloc=4586680, time=4.63 x[1] = 0.74 y[1] (analytic) = -17.069433293457112098967583375504 y[1] (numeric) = -17.069433293457112098967583375502 absolute error = 2e-30 relative error = 1.1716850616046054682666702730471e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = -17.058029108798645588196591235676 y[1] (numeric) = -17.058029108798645588196591235672 absolute error = 4e-30 relative error = 2.3449367887036687180626619386838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04169 Order of pole (three term test) = 1.875 Radius of convergence (six term test) for eq 1 = 2.086 Order of pole (six term test) = -15.05 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = -17.046619691801752842311302988558 y[1] (numeric) = -17.046619691801752842311302988556 absolute error = 2e-30 relative error = 1.1732531353191752838763559080621e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2908 Order of pole (three term test) = -36.18 Radius of convergence (six term test) for eq 1 = 1.212 Order of pole (six term test) = -10.9 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = -17.035205041609915144196974042016 y[1] (numeric) = -17.035205041609915144196974042012 absolute error = 4e-30 relative error = 2.3480785762364849551791725200859e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.029 Order of pole (three term test) = 343.6 Radius of convergence (six term test) for eq 1 = 0.9533 Order of pole (six term test) = -12.45 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = -17.023785157366528787900278674497 y[1] (numeric) = -17.023785157366528787900278674492 absolute error = 5e-30 relative error = 2.9370671409327560947468188227370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.304 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = -17.012360038214905072584917265759 y[1] (numeric) = -17.012360038214905072584917265755 absolute error = 4e-30 relative error = 2.3512316874406551625289914109908e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=140041408, alloc=4586680, time=4.76 x[1] = 0.8 y[1] (analytic) = -17.000929683298270296486888653848 y[1] (numeric) = -17.000929683298270296486888653844 absolute error = 4e-30 relative error = 2.3528125076181003527873181685829e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = -16.989494091759765750869427603131 y[1] (numeric) = -16.989494091759765750869427603127 absolute error = 4e-30 relative error = 2.3543961806020331143008597213012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01949 Order of pole (three term test) = -8.11 Radius of convergence (six term test) for eq 1 = 0.2653 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = -16.978053262742447713977607368223 y[1] (numeric) = -16.97805326274244771397760736822 absolute error = 3e-30 relative error = 1.7669870353059624248343943260477e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = -16.96660719538928744499260733859 y[1] (numeric) = -16.966607195389287444992607338587 absolute error = 3e-30 relative error = 1.7681790858075953753697188121896e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02558 Order of pole (three term test) = -2.909 Radius of convergence (six term test) for eq 1 = 0.792 Order of pole (six term test) = -11.51 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = -16.955155888843171177985645748631 y[1] (numeric) = -16.955155888843171177985645748627 absolute error = 4e-30 relative error = 2.3591643900083981688611668590483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04063 Order of pole (three term test) = -15.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=144042532, alloc=4586680, time=4.90 x[1] = 0.85 y[1] (analytic) = -16.943699342246900115871577438062 y[1] (numeric) = -16.943699342246900115871577438058 absolute error = 4e-30 relative error = 2.3607595479615969801633741083011e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2084 Order of pole (six term test) = -11.51 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = -16.932237554743190424362156647396 y[1] (numeric) = -16.932237554743190424362156647394 absolute error = 2e-30 relative error = 1.1811787978605015517590860635221e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7084 Order of pole (six term test) = -12.46 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = -16.92077052547467322591896483333 y[1] (numeric) = -16.920770525474673225918964833327 absolute error = 3e-30 relative error = 1.7729689055728399892201554157711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03333 Order of pole (three term test) = -20.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = -16.909298253583894593706003488816 y[1] (numeric) = -16.909298253583894593706003488813 absolute error = 3e-30 relative error = 1.7741717929448405881041987531013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08198 Order of pole (three term test) = -31.81 Radius of convergence (six term test) for eq 1 = 0.2372 Order of pole (six term test) = -12.07 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = -16.897820738213315545541951952668 y[1] (numeric) = -16.897820738213315545541951952664 absolute error = 4e-30 relative error = 2.3671691527382947208534619545464e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05752 Order of pole (three term test) = -15.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = -16.886337978505312037852090193456 y[1] (numeric) = -16.886337978505312037852090193452 absolute error = 4e-30 relative error = 2.3687788347548273583292801825750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7434 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop bytes used=148043608, alloc=4586680, time=5.03 x[1] = 0.91 y[1] (analytic) = -16.874849973602174959619886552531 y[1] (numeric) = -16.874849973602174959619886552526 absolute error = 5e-30 relative error = 2.9629893052807268377092565104594e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02142 Order of pole (three term test) = -24.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = -16.863356722646110126338250430944 y[1] (numeric) = -16.863356722646110126338250430939 absolute error = 5e-30 relative error = 2.9650087359448481357355145653239e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4119 Order of pole (three term test) = -53.22 Radius of convergence (six term test) for eq 1 = 0.2664 Order of pole (six term test) = -11.43 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = -16.851858224779238273960449905093 y[1] (numeric) = -16.85185822477923827396044990509 absolute error = 3e-30 relative error = 1.7802191069877105047142178569121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = -16.840354479143595052850694255885 y[1] (numeric) = -16.840354479143595052850694255882 absolute error = 3e-30 relative error = 1.7814351851770301871704691235797e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06735 Order of pole (three term test) = -19.9 Radius of convergence (six term test) for eq 1 = 0.3506 Order of pole (six term test) = -11.97 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = -16.828845484881131021734381396194 y[1] (numeric) = -16.828845484881131021734381396189 absolute error = 5e-30 relative error = 2.9710891365019369497165517702449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = -16.817331241133711641648010181442 y[1] (numeric) = -16.817331241133711641648010181438 absolute error = 4e-30 relative error = 2.3784986705954581868306955757369e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.035 Order of pole (three term test) = -26.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=152044924, alloc=4586680, time=5.17 x[1] = 0.97 y[1] (analytic) = -16.805811747043117269888757588104 y[1] (numeric) = -16.805811747043117269888757588099 absolute error = 5e-30 relative error = 2.9751612568668218564167579451328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = -16.794287001751043153963720744886 y[1] (numeric) = -16.794287001751043153963720744883 absolute error = 3e-30 relative error = 1.7863217412487992818158780440648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003087 Order of pole (three term test) = -0.8811 Radius of convergence (six term test) for eq 1 = 0.9427 Order of pole (six term test) = -13.32 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = -16.782757004399099425538823801448 y[1] (numeric) = -16.782757004399099425538823801445 absolute error = 3e-30 relative error = 1.7875489701803103239924930555818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05188 Order of pole (three term test) = -19.62 Radius of convergence (six term test) for eq 1 = 1.261 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = -16.771221754128811094387389619393 y[1] (numeric) = -16.77122175412881109438738961939 absolute error = 3e-30 relative error = 1.7887784467827736940823790110642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = -16.759681250081618042338376270378 y[1] (numeric) = -16.759681250081618042338376270373 absolute error = 5e-30 relative error = 2.9833502949082939622923895125520e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03538 Order of pole (three term test) = -5.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=156045808, alloc=4586680, time=5.31 x[1] = 1.02 y[1] (analytic) = -16.748135491398875017224278326097 y[1] (numeric) = -16.748135491398875017224278326092 absolute error = 5e-30 relative error = 2.9854069442940593746879920641871e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1964 Order of pole (six term test) = -11.51 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = -16.736584477221851626828692924975 y[1] (numeric) = -16.736584477221851626828692924971 absolute error = 4e-30 relative error = 2.3899738954766535549217600322781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01223 Order of pole (three term test) = -1.335 Radius of convergence (six term test) for eq 1 = 0.7345 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = -16.725028206691732332833550600323 y[1] (numeric) = -16.725028206691732332833550600319 absolute error = 4e-30 relative error = 2.3916252639858558739508895048110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.59 Order of pole (three term test) = -3871 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = -16.713466678949616444766010854774 y[1] (numeric) = -16.713466678949616444766010854769 absolute error = 5e-30 relative error = 2.9915995861573301685096288522790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08915 Order of pole (three term test) = -37.75 Radius of convergence (six term test) for eq 1 = 0.05455 Order of pole (six term test) = -12.04 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = -16.701899893136518113945022465788 y[1] (numeric) = -16.701899893136518113945022465783 absolute error = 5e-30 relative error = 2.9936713978597733909308987361620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09741 Order of pole (three term test) = 11.74 Radius of convergence (six term test) for eq 1 = 0.483 Order of pole (six term test) = -12.35 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = -16.69032784839336632742754850702 y[1] (numeric) = -16.690327848393366327427548507015 absolute error = 5e-30 relative error = 2.9957470251138936162393437332025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3836 Order of pole (three term test) = -82.58 Radius of convergence (six term test) for eq 1 = 0.1899 Order of pole (six term test) = -11.33 TOP MAIN SOLVE Loop bytes used=160046780, alloc=4586680, time=5.44 x[1] = 1.08 y[1] (analytic) = -16.678750543861004901954456070335 y[1] (numeric) = -16.678750543861004901954456070329 absolute error = 6e-30 relative error = 3.5973917735752916134193325714446e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3127 Order of pole (six term test) = -11.95 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = -16.667167978680192477896070673262 y[1] (numeric) = -16.667167978680192477896070673258 absolute error = 4e-30 relative error = 2.3999278132413376432786364408377e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.81 Order of pole (three term test) = -1293 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = -16.655580151991602513197395336702 y[1] (numeric) = -16.655580151991602513197395336697 absolute error = 5e-30 relative error = 3.0019969009618206200661011346985e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1606 Order of pole (six term test) = -11.96 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = -16.643987062935823277322994317626 y[1] (numeric) = -16.643987062935823277322994317622 absolute error = 4e-30 relative error = 2.4032703131015545906761318590544e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.07475 Order of pole (six term test) = -11.33 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = -16.632388710653357845201541481626 y[1] (numeric) = -16.63238871065335784520154148162 absolute error = 6e-30 relative error = 3.6074192976002822327606255962092e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = -16.620785094284624091170033300026 y[1] (numeric) = -16.620785094284624091170033300021 absolute error = 5e-30 relative error = 3.0082814810711594787356607102651e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0116 Order of pole (three term test) = -1.796 Radius of convergence (six term test) for eq 1 = 0.6544 Order of pole (six term test) = -9.881 TOP MAIN SOLVE Loop bytes used=164047556, alloc=4586680, time=5.58 x[1] = 1.14 y[1] (analytic) = -16.609176212969954682917666456428 y[1] (numeric) = -16.609176212969954682917666456422 absolute error = 6e-30 relative error = 3.6124609210387295162969409400557e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6179 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = -16.597562065849597075429380047394 y[1] (numeric) = -16.59756206584959707542938004739 absolute error = 4e-30 relative error = 2.4099924941568505847402344062650e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1681 Order of pole (three term test) = -55.79 Radius of convergence (six term test) for eq 1 = 0.8289 Order of pole (six term test) = -11.54 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = -16.58594265206371350492906236213 y[1] (numeric) = -16.585942652063713504929062362126 absolute error = 4e-30 relative error = 2.4116808335294094179366271902042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6676 Order of pole (six term test) = -10.34 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = -16.574317970752380982822422225888 y[1] (numeric) = -16.574317970752380982822422225885 absolute error = 3e-30 relative error = 1.8100292303393144344714169945448e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7395 Order of pole (six term test) = -10.62 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = -16.562688021055591289639524891937 y[1] (numeric) = -16.562688021055591289639524891933 absolute error = 4e-30 relative error = 2.4150669232644687822783429991271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2284 Order of pole (three term test) = -88.35 Radius of convergence (six term test) for eq 1 = 0.8431 Order of pole (six term test) = -11.72 TOP MAIN SOLVE Loop bytes used=168048392, alloc=4586680, time=5.72 x[1] = 1.19 y[1] (analytic) = -16.55105280211325096897699246683 y[1] (numeric) = -16.551052802113250968976992466826 absolute error = 4e-30 relative error = 2.4167646903339447794138152985101e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = -16.539412313065181321439868853802 y[1] (numeric) = -16.539412313065181321439868853798 absolute error = 4e-30 relative error = 2.4184656167258317998281661732266e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = -16.527766553051118398583149199045 y[1] (numeric) = -16.52776655305111839858314919904 absolute error = 5e-30 relative error = 3.0252121385856408762225816523515e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05078 Order of pole (three term test) = -36.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = -16.516115521210712996852973825661 y[1] (numeric) = -16.516115521210712996852973825657 absolute error = 4e-30 relative error = 2.4218769812205698390548197424680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = -16.504459216683530651527486640086 y[1] (numeric) = -16.50445921668353065152748664008 absolute error = 6e-30 relative error = 3.6353811544063804938531867999808e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.116 Order of pole (three term test) = 8.949 Radius of convergence (six term test) for eq 1 = 2.34 Order of pole (six term test) = -11.76 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = -16.492797638609051630657357995728 y[1] (numeric) = -16.492797638609051630657357995724 absolute error = 4e-30 relative error = 2.4253010845389520336529392155174e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=172049256, alloc=4586680, time=5.85 x[1] = 1.25 y[1] (analytic) = -16.481130786126670929005971998672 y[1] (numeric) = -16.481130786126670929005971998667 absolute error = 5e-30 relative error = 3.0337724182183253520716033299717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1192 Order of pole (three term test) = -37.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = -16.469458658375698261989278240135 y[1] (numeric) = -16.46945865837569826198927824013 absolute error = 5e-30 relative error = 3.0359224936984816587153258769076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02233 Order of pole (three term test) = -25.63 Radius of convergence (six term test) for eq 1 = 0.0354 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = -16.457781254495358059615307940556 y[1] (numeric) = -16.45778125449535805961530794055 absolute error = 6e-30 relative error = 3.6456919114544258195781408443986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.78 Order of pole (three term test) = -1815 Radius of convergence (six term test) for eq 1 = 0.6782 Order of pole (six term test) = -9.858 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = -16.446098573624789460423354490017 y[1] (numeric) = -16.446098573624789460423354490011 absolute error = 6e-30 relative error = 3.6482816718747020769639522502355e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04345 Order of pole (three term test) = -25.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = -16.434410614903046305422818369828 y[1] (numeric) = -16.434410614903046305422818369823 absolute error = 5e-30 relative error = 3.0423969055914313128148206564768e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3257 Order of pole (three term test) = 28.5 Radius of convergence (six term test) for eq 1 = 0.3197 Order of pole (six term test) = -12.22 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = -16.422717377469097132031716440028 y[1] (numeric) = -16.422717377469097132031716440023 absolute error = 5e-30 relative error = 3.0445631408476137086688238911871e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8957 Order of pole (six term test) = -12.37 TOP MAIN SOLVE Loop bytes used=176050004, alloc=4586680, time=5.99 x[1] = 1.31 y[1] (analytic) = -16.411018860461825168014855577587 y[1] (numeric) = -16.411018860461825168014855577581 absolute error = 6e-30 relative error = 3.6560801319017879782516246176186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = -16.39931506302002832542167065009 y[1] (numeric) = -16.399315063020028325421670650085 absolute error = 5e-30 relative error = 3.0489078237632329511837120256985e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6609 Order of pole (six term test) = -12.41 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = -16.387605984282419194523726809684 y[1] (numeric) = -16.387605984282419194523726809679 absolute error = 5e-30 relative error = 3.0510862933826756245374273410436e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.239 Order of pole (six term test) = -11.74 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = -16.375891623387625037751886092046 y[1] (numeric) = -16.375891623387625037751886092041 absolute error = 5e-30 relative error = 3.0532688631494906017341209400536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = -16.364171979474187783633138305171 y[1] (numeric) = -16.364171979474187783633138305166 absolute error = 5e-30 relative error = 3.0554555441433704518959987756386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.606 Order of pole (six term test) = -8.465 TOP MAIN SOLVE Loop bytes used=180051176, alloc=4586680, time=6.13 x[1] = 1.36 y[1] (analytic) = -16.352447051680564020727096192741 y[1] (numeric) = -16.352447051680564020727096192736 absolute error = 5e-30 relative error = 3.0576463474842090719572406563767e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8042 Order of pole (six term test) = -12.56 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = -16.340716839145124991562154856854 y[1] (numeric) = -16.34071683914512499156215485685 absolute error = 4e-30 relative error = 2.4478730274658272259131578333863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = -16.328981341006156586571315424893 y[1] (numeric) = -16.328981341006156586571315424888 absolute error = 5e-30 relative error = 3.0620403658884399164555665751110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02018 Order of pole (three term test) = 1.046 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = -16.317240556401859338027672945286 y[1] (numeric) = -16.317240556401859338027672945282 absolute error = 4e-30 relative error = 2.4513948827154181274170802334563e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.156 Order of pole (three term test) = -11.34 Radius of convergence (six term test) for eq 1 = 0.7809 Order of pole (six term test) = -12.2 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = -16.305494484470348413979568496975 y[1] (numeric) = -16.305494484470348413979568496971 absolute error = 4e-30 relative error = 2.4531608065058519144891167860359e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = -16.293743124349653612185405497309 y[1] (numeric) = -16.293743124349653612185405497306 absolute error = 3e-30 relative error = 1.8411975548557333831819255416512e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00397 Order of pole (three term test) = -23.59 Radius of convergence (six term test) for eq 1 = 0.7802 Order of pole (six term test) = -11.69 TOP MAIN SOLVE Loop bytes used=184052172, alloc=4586680, time=6.27 x[1] = 1.42 y[1] (analytic) = -16.281986475177719354048130193184 y[1] (numeric) = -16.281986475177719354048130193181 absolute error = 3e-30 relative error = 1.8425270187845766091268895983100e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5979 Order of pole (six term test) = -11.22 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = -16.27022453609240467854937632017 y[1] (numeric) = -16.270224536092404678549376320166 absolute error = 4e-30 relative error = 2.4584786713463967814447461546249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03977 Order of pole (three term test) = -15.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = -16.258457306231483236183273914403 y[1] (numeric) = -16.258457306231483236183273914399 absolute error = 4e-30 relative error = 2.4602580212003843306956540906576e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6372 Order of pole (six term test) = -11.94 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = -16.246684784732643282889922262025 y[1] (numeric) = -16.246684784732643282889922262022 absolute error = 3e-30 relative error = 1.8465305628500677745701101316035e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.639 Order of pole (six term test) = -11.02 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = -16.234906970733487673988526970928 y[1] (numeric) = -16.234906970733487673988526970924 absolute error = 4e-30 relative error = 2.4638268683711966697649622776611e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009289 Order of pole (three term test) = -25.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = -16.223123863371533858110201149559 y[1] (numeric) = -16.223123863371533858110201149556 absolute error = 3e-30 relative error = 1.8492122881298964674080111004077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4921 Order of pole (six term test) = -11.39 TOP MAIN SOLVE Loop bytes used=188052996, alloc=4586680, time=6.40 x[1] = 1.48 y[1] (analytic) = -16.211335461784213871130430677602 y[1] (numeric) = -16.211335461784213871130430677598 absolute error = 4e-30 relative error = 2.4674093071662101111315675870520e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = -16.199541765108874330101203553234 y[1] (numeric) = -16.19954176510887433010120355323 absolute error = 4e-30 relative error = 2.4692056466778192777686784966391e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0194 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = -16.187742772482776427182803301796 y[1] (numeric) = -16.187742772482776427182803301791 absolute error = 5e-30 relative error = 3.0887567650873480932103865289633e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4202 Order of pole (six term test) = -12.45 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = -16.175938483043095923575266430585 y[1] (numeric) = -16.17593848304309592357526643058 absolute error = 5e-30 relative error = 3.0910107659233480058642877345211e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4547 Order of pole (six term test) = -12.71 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = -16.164128895926923143449503914574 y[1] (numeric) = -16.164128895926923143449503914568 absolute error = 6e-30 relative error = 3.7119228871726547048905950121049e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4631 Order of pole (three term test) = -58.05 Radius of convergence (six term test) for eq 1 = 0.7276 Order of pole (six term test) = -11.99 TOP MAIN SOLVE Loop bytes used=192053744, alloc=4586680, time=6.54 x[1] = 1.53 y[1] (analytic) = -16.152314010271262967878086697801 y[1] (numeric) = -16.152314010271262967878086697795 absolute error = 6e-30 relative error = 3.7146380364971839884152267875062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = -20.48 Radius of convergence (six term test) for eq 1 = 0.7761 Order of pole (six term test) = -10.89 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = -16.140493825213034828765695195208 y[1] (numeric) = -16.140493825213034828765695195204 absolute error = 4e-30 relative error = 2.4782389208882863158524260755192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07844 Order of pole (three term test) = 9.545 Radius of convergence (six term test) for eq 1 = 0.6923 Order of pole (six term test) = -12.4 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = -16.128668339889072702779232779686 y[1] (numeric) = -16.128668339889072702779232779682 absolute error = 4e-30 relative error = 2.4800559573212171281030821318688e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = -16.116837553436125105277603239084 y[1] (numeric) = -16.116837553436125105277603239078 absolute error = 6e-30 relative error = 3.7228147148016605091470400659026e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3903 Order of pole (six term test) = -11.99 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = -16.105001464990855084241152187956 y[1] (numeric) = -16.10500146499085508424115218795 absolute error = 6e-30 relative error = 3.7255507322013192904482169725521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8336 Order of pole (three term test) = -119.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = -16.093160073689840214200772418816 y[1] (numeric) = -16.093160073689840214200772418811 absolute error = 5e-30 relative error = 3.1069100022029420187062722799402e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01016 Order of pole (three term test) = -0.1528 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=196054736, alloc=4586680, time=6.68 x[1] = 1.59 y[1] (analytic) = -16.081313378669572590166673177636 y[1] (numeric) = -16.081313378669572590166673177632 absolute error = 4e-30 relative error = 2.4873590270964081310469069446816e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07117 Order of pole (three term test) = -27.49 Radius of convergence (six term test) for eq 1 = 0.7437 Order of pole (six term test) = -10.81 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = -16.069461379066458821556813348372 y[1] (numeric) = -16.069461379066458821556813348368 absolute error = 4e-30 relative error = 2.4891935738498140441285259035288e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9879 Order of pole (six term test) = -12.34 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = -16.05760407401682002612499853127 y[1] (numeric) = -16.057604074016820026124998531265 absolute error = 5e-30 relative error = 3.1137895647150844042023640989329e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05945 Order of pole (three term test) = -36.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = -16.045741462656891823888641999707 y[1] (numeric) = -16.045741462656891823888641999704 absolute error = 3e-30 relative error = 1.8696549529866679680327354926441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.42 Order of pole (six term test) = -9.106 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = -16.033873544122824331056189520355 y[1] (numeric) = -16.033873544122824331056189520351 absolute error = 4e-30 relative error = 2.4947184403023995731967534907575e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01383 Order of pole (three term test) = -22.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = -16.022000317550682153954208021369 y[1] (numeric) = -16.022000317550682153954208021366 absolute error = 3e-30 relative error = 1.8724253779434554956734604775838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=200058144, alloc=4586680, time=6.82 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = -16.01012178207644438295413809343 y[1] (numeric) = -16.010121782076444382954138093426 absolute error = 4e-30 relative error = 2.4984194714109270768036302636368e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.479 Order of pole (three term test) = -309.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = -15.998237936836004586398710308338 y[1] (numeric) = -15.998237936836004586398710308333 absolute error = 5e-30 relative error = 3.1253441908670958725488817850549e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = -15.986348780965170804528025339951 y[1] (numeric) = -15.986348780965170804528025339947 absolute error = 4e-30 relative error = 2.5021348244089175013287590538364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1699 Order of pole (six term test) = -12.02 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = -15.97445431359966554340529787222 y[1] (numeric) = -15.974454313599665543405297872214 absolute error = 6e-30 relative error = 3.7559968448449409084367434335695e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5806 Order of pole (six term test) = -11.27 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = -15.962554533875125768842264279046 y[1] (numeric) = -15.962554533875125768842264279041 absolute error = 5e-30 relative error = 3.1323307240010928560873031350723e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02596 Order of pole (three term test) = -21.87 Radius of convergence (six term test) for eq 1 = 0.7056 Order of pole (six term test) = -11.4 TOP MAIN SOLVE Loop bytes used=204058848, alloc=4586680, time=6.95 x[1] = 1.7 y[1] (analytic) = -15.950649440927102900324254060774 y[1] (numeric) = -15.95064944092710290032425406077 absolute error = 4e-30 relative error = 2.5077348824033256239176412258646e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.535 Order of pole (six term test) = 0.6553 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = -15.938739033891062804934925022016 y[1] (numeric) = -15.938739033891062804934925022012 absolute error = 4e-30 relative error = 2.5096088162900898240001402503792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.026 Order of pole (six term test) = -12.1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = -15.926823311902385791280662175595 y[1] (numeric) = -15.926823311902385791280662175591 absolute error = 4e-30 relative error = 2.5114863910185604975316035736031e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = -15.91490227409636660341464035736 y[1] (numeric) = -15.914902274096366603414640357355 absolute error = 5e-30 relative error = 3.1417095209803261984232331941447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = -15.902975919608214414760550536609 y[1] (numeric) = -15.902975919608214414760550536603 absolute error = 6e-30 relative error = 3.7728787557315347749927150269034e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03594 Order of pole (three term test) = -39.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = -15.891044247573052822035989806889 y[1] (numeric) = -15.891044247573052822035989806885 absolute error = 4e-30 relative error = 2.5171410624011677771227554551580e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.599 Order of pole (six term test) = -12.24 TOP MAIN SOLVE Loop bytes used=208060064, alloc=4586680, time=7.09 x[1] = 1.76 y[1] (analytic) = -15.879107257125919839175515041926 y[1] (numeric) = -15.879107257125919839175515041923 absolute error = 3e-30 relative error = 1.8892749771267637202232844048191e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3072 Order of pole (six term test) = -11.13 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = -15.867164947401767891253360201413 y[1] (numeric) = -15.867164947401767891253360201409 absolute error = 4e-30 relative error = 2.5209292354744165739253720842908e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04588 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = -15.855217317535463808405817271434 y[1] (numeric) = -15.855217317535463808405817271429 absolute error = 5e-30 relative error = 3.1535360883827988944473048203458e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.373 Order of pole (three term test) = -321.3 Radius of convergence (six term test) for eq 1 = 1.336 Order of pole (six term test) = -14.07 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = -15.843264366661788819753280824264 y[1] (numeric) = -15.84326436666178881975328082426 absolute error = 4e-30 relative error = 2.5247322189592478106491931787360e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = -15.831306093915438547321956182299 y[1] (numeric) = -15.831306093915438547321956182293 absolute error = 6e-30 relative error = 3.7899589360514125899903556511445e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = -15.819342498431022999965231170839 y[1] (numeric) = -15.819342498431022999965231170834 absolute error = 5e-30 relative error = 3.1606876205480124209292802334903e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02851 Order of pole (three term test) = -25.27 NO COMPLEX POLE (six term test) for Equation 1 bytes used=212062592, alloc=4586680, time=7.23 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = -15.807373579343066567284711444525 y[1] (numeric) = -15.807373579343066567284711444522 absolute error = 3e-30 relative error = 1.8978484850388890549678593312350e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.061 Order of pole (six term test) = -13.03 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = -15.795399335786008013550919372129 y[1] (numeric) = -15.795399335786008013550919372124 absolute error = 5e-30 relative error = 3.1654786901601249312643271654565e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02097 Order of pole (three term test) = -26.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = -15.783419766894200471623656464452 y[1] (numeric) = -15.783419766894200471623656464446 absolute error = 6e-30 relative error = 3.8014575349412103369004617521510e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04698 Order of pole (three term test) = 2.083 Radius of convergence (six term test) for eq 1 = 0.3129 Order of pole (six term test) = -12.13 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = -15.771434871801911436872029330114 y[1] (numeric) = -15.771434871801911436872029330109 absolute error = 5e-30 relative error = 3.1702885886049644342859864763400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.123 Order of pole (six term test) = -13.39 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = -15.75944464964332276109413914394 y[1] (numeric) = -15.759444649643322761094139143934 absolute error = 6e-30 relative error = 3.8072407584081940426472382261476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4459 Order of pole (three term test) = -67.72 Radius of convergence (six term test) for eq 1 = 0.4663 Order of pole (six term test) = -11.78 TOP MAIN SOLVE Loop bytes used=216063552, alloc=4586680, time=7.36 x[1] = 1.87 y[1] (analytic) = -15.747449099552530646436434612696 y[1] (numeric) = -15.747449099552530646436434612692 absolute error = 4e-30 relative error = 2.5400939382072118710655373447090e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.108 Order of pole (three term test) = -23.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = -15.735448220663545639312728422948 y[1] (numeric) = -15.735448220663545639312728422944 absolute error = 4e-30 relative error = 2.5420311794787404089503521054823e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08372 Order of pole (three term test) = 0.02676 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = -15.723442012110292624322877155743 y[1] (numeric) = -15.723442012110292624322877155739 absolute error = 4e-30 relative error = 2.5439722402506875875148680344144e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = -15.711430473026610818171124652897 y[1] (numeric) = -15.711430473026610818171124652894 absolute error = 3e-30 relative error = 1.9094378485462549197765381701338e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = -15.699413602546253763584108819617 y[1] (numeric) = -15.699413602546253763584108819614 absolute error = 3e-30 relative error = 1.9108993978688710523777639510450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04181 Order of pole (three term test) = -22.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = -15.687391399802889323228531848186 y[1] (numeric) = -15.687391399802889323228531848181 absolute error = 5e-30 relative error = 3.1872730606204066247772945211661e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.63 Order of pole (six term test) = -28.69 TOP MAIN SOLVE Loop bytes used=220064556, alloc=4586680, time=7.50 x[1] = 1.93 y[1] (analytic) = -15.675363863930099673628493847471 y[1] (numeric) = -15.675363863930099673628493847467 absolute error = 4e-30 relative error = 2.5517748964055798518773934812024e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05525 Order of pole (three term test) = -2.555 Radius of convergence (six term test) for eq 1 = 0.822 Order of pole (six term test) = -12.09 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = -15.663330994061381299082489863012 y[1] (numeric) = -15.663330994061381299082489863007 absolute error = 5e-30 relative error = 3.1921690232401444276382529186464e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1077 Order of pole (three term test) = 14.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = -15.651292789330144985580070272372 y[1] (numeric) = -15.651292789330144985580070272368 absolute error = 4e-30 relative error = 2.5556994261374333459100982382022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03111 Order of pole (three term test) = -26.65 Radius of convergence (six term test) for eq 1 = 0.9129 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = -15.639249248869715814718164540567 y[1] (numeric) = -15.639249248869715814718164540562 absolute error = 5e-30 relative error = 3.1970844127069343786239427523858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = -15.627200371813333157617068320243 y[1] (numeric) = -15.62720037181333315761706832024 absolute error = 3e-30 relative error = 1.9197296563823920919253553664106e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04042 Order of pole (three term test) = -30.08 Radius of convergence (six term test) for eq 1 = 0.2396 Order of pole (six term test) = -11.17 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = -15.61514615729415066883609388141 y[1] (numeric) = -15.615146157294150668836093881406 absolute error = 4e-30 relative error = 2.5616154723800129650940501673004e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = -9.621 bytes used=224065364, alloc=4586680, time=7.64 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = -15.603086604445236280288883855391 y[1] (numeric) = -15.603086604445236280288883855388 absolute error = 3e-30 relative error = 1.9226964997716003039572205308140e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.181 Order of pole (six term test) = -12.43 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = -15.59102171239957219515838827781 y[1] (numeric) = -15.591021712399572195158388277807 absolute error = 3e-30 relative error = 1.9241843513142526906421349143729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.32 Order of pole (six term test) = -459.2 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = -15.578951480290054881811504915282 y[1] (numeric) = -15.578951480290054881811504915279 absolute error = 3e-30 relative error = 1.9256751674177143349641721156246e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07614 Order of pole (three term test) = -26.4 Radius of convergence (six term test) for eq 1 = 0.4869 Order of pole (six term test) = -11.6 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = -15.566875907249495067713382860592 y[1] (numeric) = -15.566875907249495067713382860589 absolute error = 3e-30 relative error = 1.9271689566195487017620687390263e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5896 Order of pole (six term test) = -12.11 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = -15.554794992410617733341389381074 y[1] (numeric) = -15.55479499241061773334138938107 absolute error = 4e-30 relative error = 2.5715543033203914694709520058536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02382 Order of pole (three term test) = 0.3144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=228066096, alloc=4586680, time=7.78 x[1] = 2.04 y[1] (analytic) = -15.542708734906062106098740004929 y[1] (numeric) = -15.542708734906062106098740004925 absolute error = 4e-30 relative error = 2.5735539848448272579160261962056e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = -15.530617133868381654227791830233 y[1] (numeric) = -15.530617133868381654227791830229 absolute error = 4e-30 relative error = 2.5755576649153258715119572934092e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = -15.518520188430044080723000041343 y[1] (numeric) = -15.51852018843004408072300004134 absolute error = 3e-30 relative error = 1.9331740163193355351695445737074e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04031 Order of pole (three term test) = -26.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = -15.506417897723431317243537617461 y[1] (numeric) = -15.506417897723431317243537617458 absolute error = 3e-30 relative error = 1.9346828002361808057607725241436e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01084 Order of pole (three term test) = -23.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = -15.494310260880839518025578218066 y[1] (numeric) = -15.494310260880839518025578218063 absolute error = 3e-30 relative error = 1.9361946091748470818119983167809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7153 Order of pole (six term test) = -11.76 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = -15.482197277034479053794242229966 y[1] (numeric) = -15.482197277034479053794242229963 absolute error = 3e-30 relative error = 1.9377094519070950610759410776241e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=232067292, alloc=4586680, time=7.91 x[1] = 2.1 y[1] (analytic) = -15.470078945316474505675205960693 y[1] (numeric) = -15.47007894531647450567520596069 absolute error = 3e-30 relative error = 1.9392273372387941609858091576702e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = -15.457955264858864659105973962972 y[1] (numeric) = -15.457955264858864659105973962969 absolute error = 3e-30 relative error = 1.9407482740100883691645168228978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.08214 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = -15.445826234793602497746814474995 y[1] (numeric) = -15.445826234793602497746814474992 absolute error = 3e-30 relative error = 1.9422722710955630626677023629017e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02533 Order of pole (three term test) = -22.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = -15.433691854252555197391357961238 y[1] (numeric) = -15.433691854252555197391357961235 absolute error = 3e-30 relative error = 1.9437993374044128025683619243676e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04448 Order of pole (three term test) = -0.3279 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = -15.421552122367504119876858738537 y[1] (numeric) = -15.421552122367504119876858738534 absolute error = 3e-30 relative error = 1.9453294818806101105424750554575e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9313 Order of pole (six term test) = -11.78 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = -15.409407038270144806994119672169 y[1] (numeric) = -15.409407038270144806994119672165 absolute error = 4e-30 relative error = 2.5958169513374336455560169394890e-29 % Correct digits = 31 h = 0.01 bytes used=236068352, alloc=4586680, time=8.05 NO INFO (given) for Equation 1 NO 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] = 2.16 y[1] (analytic) = -15.397256601092086974397079926645 y[1] (numeric) = -15.397256601092086974397079926641 absolute error = 4e-30 relative error = 2.5978653883811292102589209070019e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09236 Order of pole (three term test) = -37.76 Radius of convergence (six term test) for eq 1 = 0.7792 Order of pole (six term test) = -11.39 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = -15.38510080996485450551206575597 y[1] (numeric) = -15.385100809964854505512065755968 absolute error = 2e-30 relative error = 1.2999589828521694100791772144688e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05169 Order of pole (three term test) = -25.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = -15.372939664019885445446704318079 y[1] (numeric) = -15.372939664019885445446704318077 absolute error = 2e-30 relative error = 1.3009873477100592416057152538510e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02841 Order of pole (three term test) = -1.207 Radius of convergence (six term test) for eq 1 = 1.122 Order of pole (six term test) = -12.13 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = -15.360773162388531994898500498166 y[1] (numeric) = -15.360773162388531994898500498163 absolute error = 3e-30 relative error = 1.9530266922667799658223719392743e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = -15.348601304202060504063076725665 y[1] (numeric) = -15.348601304202060504063076725662 absolute error = 3e-30 relative error = 1.9545754955395678632934237134757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=240069412, alloc=4586680, time=8.19 x[1] = 2.21 y[1] (analytic) = -15.336424088591651466542075769583 y[1] (numeric) = -15.33642408859165146654207576958 absolute error = 3e-30 relative error = 1.9561274405756804559120379931006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5297 Order of pole (three term test) = -90.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = -15.324241514688399513250726496912 y[1] (numeric) = -15.32424151468839951325072649691 absolute error = 2e-30 relative error = 1.3051216910690066577304356349091e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5229 Order of pole (three term test) = -33.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = -15.312053581623313406325072578861 y[1] (numeric) = -15.312053581623313406325072578859 absolute error = 2e-30 relative error = 1.3061605285918606420605399518086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1612 Order of pole (three term test) = -40.47 Radius of convergence (six term test) for eq 1 = 1.105 Order of pole (six term test) = -12.34 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = -15.299860288527316033028864129605 y[1] (numeric) = -15.299860288527316033028864129603 absolute error = 2e-30 relative error = 1.3072014791531860883384478706471e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3373 Order of pole (six term test) = -11.38 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = -15.287661634531244399660112262302 y[1] (numeric) = -15.2876616345312443996601122623 absolute error = 2e-30 relative error = 1.3082445489782876764297055235580e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1515 Order of pole (three term test) = -60.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = -15.275457618765849625457306547086 y[1] (numeric) = -15.275457618765849625457306547083 absolute error = 3e-30 relative error = 1.9639346164755875014172378905828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09743 Order of pole (three term test) = -7.236 Radius of convergence (six term test) for eq 1 = 0.9217 Order of pole (six term test) = -11.87 TOP MAIN SOLVE Loop bytes used=244070100, alloc=4586680, time=8.33 x[1] = 2.27 y[1] (analytic) = -15.263248240361796936505295355752 y[1] (numeric) = -15.263248240361796936505295355749 absolute error = 3e-30 relative error = 1.9655056071661510297655557267876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = -15.25103349844966565964082907788 y[1] (numeric) = -15.251033498449665659640829077878 absolute error = 2e-30 relative error = 1.3113865366588492236455250542809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = -15.23881339215994921635776619309 y[1] (numeric) = -15.238813392159949216357766193087 absolute error = 3e-30 relative error = 1.9686572194285397953559602255948e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = -15.226587920623055116711942184154 y[1] (numeric) = -15.226587920623055116711942184151 absolute error = 3e-30 relative error = 1.9702378600111503654707472705014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01437 Order of pole (three term test) = -26.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = -15.214357082969304953225701275712 y[1] (numeric) = -15.21435708296930495322570127571 absolute error = 2e-30 relative error = 1.3145478241987407485216332728629e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1266 Order of pole (three term test) = -20.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 bytes used=248072208, alloc=4586680, time=8.46 y[1] (analytic) = -15.202120878328934394792090983276 y[1] (numeric) = -15.202120878328934394792090983275 absolute error = 1e-30 relative error = 6.5780295262980647271000235984385e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1496 Order of pole (three term test) = -21.59 Radius of convergence (six term test) for eq 1 = 0.844 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = -15.189879305832093180578719457258 y[1] (numeric) = -15.189879305832093180578719457256 absolute error = 2e-30 relative error = 1.3166661562821687654126368906878e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = -15.177632364608845113931275606732 y[1] (numeric) = -15.177632364608845113931275606731 absolute error = 1e-30 relative error = 6.5886429185872021792226013531138e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06083 Order of pole (three term test) = -26.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = -15.165380053789168056276711987674 y[1] (numeric) = -15.165380053789168056276711987671 absolute error = 3e-30 relative error = 1.9781897910632517537501754431879e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.438 Order of pole (three term test) = -29.16 Radius of convergence (six term test) for eq 1 = 1.924 Order of pole (six term test) = -10.21 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = -15.153122372502953921026090440341 y[1] (numeric) = -15.153122372502953921026090440338 absolute error = 3e-30 relative error = 1.9797899906383899201708509045415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04264 Order of pole (three term test) = -3.459 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = -15.140859319880008667477090460575 y[1] (numeric) = -15.140859319880008667477090460573 absolute error = 2e-30 relative error = 1.3209289893962570698798221930172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05496 Order of pole (three term test) = -20.74 Radius of convergence (six term test) for eq 1 = 0.5733 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop bytes used=252073504, alloc=4586680, time=8.60 x[1] = 2.38 y[1] (analytic) = -15.128590895050052294716180289695 y[1] (numeric) = -15.128590895050052294716180289692 absolute error = 3e-30 relative error = 1.9830002812631907239831503402290e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8717 Order of pole (six term test) = -11.3 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = -15.116317097142718835520450707703 y[1] (numeric) = -15.1163170971427188355204507077 absolute error = 3e-30 relative error = 1.9846103920160943098989343618293e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = -15.104037925287556350259111514545 y[1] (numeric) = -15.104037925287556350259111514543 absolute error = 2e-30 relative error = 1.3241492175092795580235258956378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.66 Order of pole (six term test) = -15.1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = -15.091753378614026920794650684109 y[1] (numeric) = -15.091753378614026920794650684106 absolute error = 3e-30 relative error = 1.9878405939572207314307623358137e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01783 Order of pole (three term test) = -26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = -15.079463456251506644383656175679 y[1] (numeric) = -15.079463456251506644383656175677 absolute error = 2e-30 relative error = 1.3263071367243230475998422972852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8816 Order of pole (six term test) = -11.69 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = -15.067168157329285627577300387588 y[1] (numeric) = -15.067168157329285627577300387585 absolute error = 3e-30 relative error = 1.9910841696823284879747377740864e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2421 Order of pole (three term test) = -64.98 Radius of convergence (six term test) for eq 1 = 1.182 Order of pole (six term test) = -12.24 TOP MAIN SOLVE Loop bytes used=256074356, alloc=4586680, time=8.74 x[1] = 2.44 y[1] (analytic) = -15.05486748097656798012148723773 y[1] (numeric) = -15.054867480976567980121487237728 absolute error = 2e-30 relative error = 1.3284739985438021823489450951171e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7603 Order of pole (three term test) = -109.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = -15.042561426322471808856661855696 y[1] (numeric) = -15.042561426322471808856661855694 absolute error = 2e-30 relative error = 1.3295607997320638046983030779062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03477 Order of pole (three term test) = 0.5019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = -15.030249992496029211617282871202 y[1] (numeric) = -15.030249992496029211617282871201 absolute error = 1e-30 relative error = 6.6532492839391086824575307521196e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = -15.017933178626186271130957283552 y[1] (numeric) = -15.01793317862618627113095728355 absolute error = 2e-30 relative error = 1.3317411765065240696180054396833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1017 Order of pole (three term test) = -23.49 Radius of convergence (six term test) for eq 1 = 1.325 Order of pole (six term test) = -9.993 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = -15.005610983841803048917237896817 y[1] (numeric) = -15.005610983841803048917237896816 absolute error = 1e-30 relative error = 6.6641738285552673088784760585449e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6433 Order of pole (six term test) = -12.25 TOP MAIN SOLVE Loop bytes used=260075292, alloc=4586680, time=8.88 x[1] = 2.49 y[1] (analytic) = -14.993283407271653579186083305472 y[1] (numeric) = -14.99328340727165357918608330547 absolute error = 2e-30 relative error = 1.3339306312518656554488538271073e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05278 Order of pole (three term test) = -4.304 Radius of convergence (six term test) for eq 1 = 0.6609 Order of pole (six term test) = -10.58 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = -14.980950448044425862735980415159 y[1] (numeric) = -14.980950448044425862735980415157 absolute error = 2e-30 relative error = 1.3350287800071288370548664069321e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2507 Order of pole (three term test) = -27.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = -14.96861210528872186085172948333 y[1] (numeric) = -14.96861210528872186085172948333 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -18.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = -14.956268378133057489201891664443 y[1] (numeric) = -14.956268378133057489201891664442 absolute error = 1e-30 relative error = 6.6861597740654260656020014058936e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0649 Order of pole (three term test) = 3.516 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = -14.943919265705862611735899044418 y[1] (numeric) = -14.943919265705862611735899044417 absolute error = 1e-30 relative error = 6.6916849737997155706314545321850e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.384 Order of pole (six term test) = -11.86 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = -14.931564767135481034580827149095 y[1] (numeric) = -14.931564767135481034580827149092 absolute error = 3e-30 relative error = 2.0091665185707991672952617790142e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.863 Order of pole (six term test) = -10.77 TOP MAIN SOLVE Loop bytes used=264076316, alloc=4586680, time=9.02 x[1] = 2.55 y[1] (analytic) = -14.919204881550170499937829911348 y[1] (numeric) = -14.919204881550170499937829911346 absolute error = 2e-30 relative error = 1.3405540146937048238222595283737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.659 Order of pole (six term test) = -13.53 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = -14.906839608078102679978237081619 y[1] (numeric) = -14.906839608078102679978237081616 absolute error = 3e-30 relative error = 2.0124990131203146727800860439349e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = -14.894468945847363170739314066506 y[1] (numeric) = -14.894468945847363170739314066504 absolute error = 2e-30 relative error = 1.3427803349495101718627125501028e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.373 Order of pole (six term test) = -12.05 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = -14.882092893985951486019684180188 y[1] (numeric) = -14.882092893985951486019684180185 absolute error = 3e-30 relative error = 2.0158455006098902014888521488736e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7 Order of pole (six term test) = -12 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = -14.869711451621781051274413293314 y[1] (numeric) = -14.869711451621781051274413293312 absolute error = 2e-30 relative error = 1.3450160122521192916402448969340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1036 Order of pole (three term test) = -28.74 Radius of convergence (six term test) for eq 1 = 0.8103 Order of pole (six term test) = -12.08 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = -14.857324617882679197509756864126 y[1] (numeric) = -14.857324617882679197509756864124 absolute error = 2e-30 relative error = 1.3461373776492341777147215615715e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.197 Order of pole (six term test) = -11.6 TOP MAIN SOLVE Loop bytes used=268077464, alloc=4586680, time=9.16 x[1] = 2.61 y[1] (analytic) = -14.844932391896387155177569336463 y[1] (numeric) = -14.84493239189638715517756933646 absolute error = 3e-30 relative error = 2.0208916556855808638783792629091e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.177 Order of pole (six term test) = -12.51 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = -14.832534772790560048069375889385 y[1] (numeric) = -14.832534772790560048069375889381 absolute error = 4e-30 relative error = 2.6967743957949602104615968963447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01742 Order of pole (three term test) = -23.82 Radius of convergence (six term test) for eq 1 = 1.166 Order of pole (six term test) = -11.13 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = -14.820131759692766887210106523101 y[1] (numeric) = -14.820131759692766887210106523098 absolute error = 3e-30 relative error = 2.0242735008330265917149326198648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.331 Order of pole (six term test) = -13.83 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = -14.807723351730490564751492465911 y[1] (numeric) = -14.807723351730490564751492465908 absolute error = 3e-30 relative error = 2.0259697785678902769152960585027e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03166 Order of pole (three term test) = -13.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = -14.795309548031127847865124886843 y[1] (numeric) = -14.79530954803112784786512488684 absolute error = 3e-30 relative error = 2.0276696410175630485493153471379e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3572 Order of pole (three term test) = -51.69 Radius of convergence (six term test) for eq 1 = 0.4596 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop bytes used=272078512, alloc=4586680, time=9.29 x[1] = 2.66 y[1] (analytic) = -14.782890347721989372635175898713 y[1] (numeric) = -14.782890347721989372635175898709 absolute error = 4e-30 relative error = 2.7058307989251852440211480330216e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1424 Order of pole (three term test) = -6.343 Radius of convergence (six term test) for eq 1 = 0.7858 Order of pole (six term test) = -9.893 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = -14.770465749930299637950781836278 y[1] (numeric) = -14.770465749930299637950781836273 absolute error = 5e-30 relative error = 3.3851336069233933965817927092852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2548 Order of pole (three term test) = -23.44 Radius of convergence (six term test) for eq 1 = 1.347 Order of pole (six term test) = -11.87 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = -14.7580357537831969993980887942 y[1] (numeric) = -14.758035753783196999398088794197 absolute error = 3e-30 relative error = 2.0327908470007298747208238284694e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005152 Order of pole (three term test) = -25.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = -14.745600358407733663151960409521 y[1] (numeric) = -14.745600358407733663151960409517 absolute error = 4e-30 relative error = 2.7126735451766508317904128289451e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07353 Order of pole (three term test) = 3.089 Radius of convergence (six term test) for eq 1 = 2.165 Order of pole (six term test) = -12.13 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = -14.733159562930875679867347873309 y[1] (numeric) = -14.733159562930875679867347873306 absolute error = 3e-30 relative error = 2.0362231109938568536893164309293e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.378 Order of pole (six term test) = -11.08 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = -14.720713366479502938570322156233 y[1] (numeric) = -14.72071336647950293857032215623 absolute error = 3e-30 relative error = 2.0379447145756482030476294133342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=276079824, alloc=4586680, time=9.43 x[1] = 2.72 y[1] (analytic) = -14.708261768180409160548768432703 y[1] (numeric) = -14.708261768180409160548768432699 absolute error = 4e-30 relative error = 2.7195599745535727174534714132352e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5972 Order of pole (three term test) = -51.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = -14.695804767160301893242742688308 y[1] (numeric) = -14.695804767160301893242742688304 absolute error = 4e-30 relative error = 2.7218652284620187925994068852872e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0147 Order of pole (three term test) = -26.99 Radius of convergence (six term test) for eq 1 = 1.67 Order of pole (six term test) = -12.73 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = -14.683342362545802504134490495236 y[1] (numeric) = -14.683342362545802504134490495231 absolute error = 5e-30 relative error = 3.4052192454178385252803099888608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01935 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = -14.670874553463446174638127940358 y[1] (numeric) = -14.670874553463446174638127940353 absolute error = 5e-30 relative error = 3.4081131167600491589660127153512e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09498 Order of pole (three term test) = -24.54 Radius of convergence (six term test) for eq 1 = 0.1947 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = -14.658401339039681893988984690692 y[1] (numeric) = -14.658401339039681893988984690688 absolute error = 4e-30 relative error = 2.7288105349843372595649686440402e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.779 Order of pole (six term test) = -11.91 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = -14.645922718400872453132609180923 y[1] (numeric) = -14.64592271840087245313260918092 absolute error = 3e-30 relative error = 2.0483516523208566781852866530671e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1018 Order of pole (three term test) = -5.771 Radius of convergence (six term test) for eq 1 = 1.385 Order of pole (six term test) = -12.3 TOP MAIN SOLVE Loop bytes used=280080844, alloc=4586680, time=9.57 x[1] = 2.78 y[1] (analytic) = -14.633438690673294438613435907674 y[1] (numeric) = -14.633438690673294438613435907671 absolute error = 3e-30 relative error = 2.0500991348752956475387568110474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = -14.620949254983138226463114815221 y[1] (numeric) = -14.620949254983138226463114815218 absolute error = 3e-30 relative error = 2.0518503605212463228749975903750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1562 Order of pole (three term test) = -33.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = -14.60845441045650797608850275735 y[1] (numeric) = -14.608454410456507976088502757347 absolute error = 3e-30 relative error = 2.0536053409268580372787664631649e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.914 Order of pole (six term test) = -8.971 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = -14.595954156219421624159317020035 y[1] (numeric) = -14.595954156219421624159317020032 absolute error = 3e-30 relative error = 2.0553640878090059050206169228624e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09754 Order of pole (three term test) = -8.875 Radius of convergence (six term test) for eq 1 = 1.555 Order of pole (six term test) = -10.49 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = -14.583448491397810878495450889634 y[1] (numeric) = -14.583448491397810878495450889632 absolute error = 2e-30 relative error = 1.3714177419556968834147580797593e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3826 Order of pole (three term test) = -69.95 Radius of convergence (six term test) for eq 1 = 0.1229 Order of pole (six term test) = -11.6 TOP MAIN SOLVE Loop bytes used=284081984, alloc=4586680, time=9.71 x[1] = 2.83 y[1] (analytic) = -14.570937415117521211953951251293 y[1] (numeric) = -14.570937415117521211953951251289 absolute error = 4e-30 relative error = 2.7451905708207574424663456247061e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06851 Order of pole (three term test) = 1.737 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = -14.55842092650431185631565820223 y[1] (numeric) = -14.558420926504311856315658202227 absolute error = 3e-30 relative error = 2.0606630452196600538395640641544e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.44 Order of pole (six term test) = -11.87 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = -14.545899024683855796171506664629 y[1] (numeric) = -14.545899024683855796171506664626 absolute error = 3e-30 relative error = 2.0624369761601605436536157478789e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = -14.533371708781739762808489982775 y[1] (numeric) = -14.533371708781739762808489982772 absolute error = 3e-30 relative error = 2.0642147329014232396673970002415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03589 Order of pole (three term test) = 1.082 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = -14.52083897792346422809528548916 y[1] (numeric) = -14.520838977923464228095285489158 absolute error = 2e-30 relative error = 1.3773308849720525481919258007966e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.174 Order of pole (six term test) = -12.42 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = -14.508300831234443398367542024237 y[1] (numeric) = -14.508300831234443398367542024234 absolute error = 3e-30 relative error = 2.0677817718952992266027550535953e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1263 Order of pole (three term test) = -5.132 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=288083060, alloc=4586680, time=9.85 x[1] = 2.89 y[1] (analytic) = -14.495757267840005208312829394485 y[1] (numeric) = -14.495757267840005208312829394482 absolute error = 3e-30 relative error = 2.0695710783290635736629700556563e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = -14.483208286865391314855249753507 y[1] (numeric) = -14.483208286865391314855249753504 absolute error = 3e-30 relative error = 2.0713642589264257827040609053844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.947 Order of pole (six term test) = -7.509 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = -14.470653887435757091039710890817 y[1] (numeric) = -14.470653887435757091039710890814 absolute error = 3e-30 relative error = 2.0731613259057838767149600607920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02423 Order of pole (three term test) = -26.65 Radius of convergence (six term test) for eq 1 = 0.3867 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = -14.458094068676171619915861413012 y[1] (numeric) = -14.458094068676171619915861413007 absolute error = 5e-30 relative error = 3.4582704858952516564471002810505e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03597 Order of pole (three term test) = -9.334 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = -14.445528829711617688421687802001 y[1] (numeric) = -14.445528829711617688421687801998 absolute error = 3e-30 relative error = 2.0767671681424281174314653860545e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = -14.432958169666991781266773335009 y[1] (numeric) = -14.432958169666991781266773335006 absolute error = 3e-30 relative error = 2.0785759680956785368856392998253e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=292085076, alloc=4586680, time=9.99 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = -14.420382087667104074815218850979 y[1] (numeric) = -14.420382087667104074815218850974 absolute error = 5e-30 relative error = 3.4673145063723400884761239418466e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09714 Order of pole (three term test) = 10.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = -14.407800582836678430968225348102 y[1] (numeric) = -14.407800582836678430968225348099 absolute error = 3e-30 relative error = 2.0822053878048229404052613336876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5081 Order of pole (six term test) = -12.42 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = -14.395213654300352391046338397158 y[1] (numeric) = -14.395213654300352391046338397154 absolute error = 4e-30 relative error = 2.7787013767628662385593739182202e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04829 Order of pole (three term test) = -27.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = -14.382621301182677169671354355293 y[1] (numeric) = -14.38262130118267716967135435529 absolute error = 3e-30 relative error = 2.0858506507108764697892801961180e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4445 Order of pole (three term test) = -31.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = -14.370023522608117648647888364991 y[1] (numeric) = -14.370023522608117648647888364987 absolute error = 4e-30 relative error = 2.7835723398134087294969543329937e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=296085908, alloc=4586680, time=10.12 x[1] = 3 y[1] (analytic) = -14.357420317701052370844604122844 y[1] (numeric) = -14.35742031770105237084460412284 absolute error = 4e-30 relative error = 2.7860158102834523996049307054497e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1018 Order of pole (three term test) = -18.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = -14.344811685585773534075105402864 y[1] (numeric) = -14.34481168558577353407510540286 absolute error = 4e-30 relative error = 2.7884646293540096214528920731253e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = -14.332197625386486984978489318965 y[1] (numeric) = -14.332197625386486984978489318962 absolute error = 3e-30 relative error = 2.0931891105702646666976790798766e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02787 Order of pole (three term test) = -21.39 Radius of convergence (six term test) for eq 1 = 1.285 Order of pole (six term test) = -11.76 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = -14.319578136227312212899561311325 y[1] (numeric) = -14.319578136227312212899561311321 absolute error = 4e-30 relative error = 2.7933783816440380488177461483347e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.965 Order of pole (six term test) = -12.5 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = -14.306953217232282343768711841282 y[1] (numeric) = -14.306953217232282343768711841278 absolute error = 4e-30 relative error = 2.7958433492199609639663660861474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.014 Order of pole (six term test) = -12.47 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = -14.294322867525344133981454779464 y[1] (numeric) = -14.294322867525344133981454779459 absolute error = 5e-30 relative error = 3.4978921676376041848385030734832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.191 Order of pole (three term test) = 2.854 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=300086932, alloc=4586680, time=10.26 x[1] = 3.06 y[1] (analytic) = -14.281687086230357964277627471804 y[1] (numeric) = -14.2816870862303579642776274718 absolute error = 4e-30 relative error = 2.8007895536771611227587488628176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1035 Order of pole (three term test) = -4.314 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = -14.269045872471097833620252468141 y[1] (numeric) = -14.269045872471097833620252468137 absolute error = 4e-30 relative error = 2.8032708253584753201445707133262e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.049 Order of pole (six term test) = -11.23 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = -14.256399225371251353074060898052 y[1] (numeric) = -14.256399225371251353074060898047 absolute error = 5e-30 relative error = 3.5071969583327902620320820059370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03917 Order of pole (three term test) = -0.0833 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = -14.243747144054419739683677478613 y[1] (numeric) = -14.243747144054419739683677478609 absolute error = 4e-30 relative error = 2.8082497951879660085307626614089e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0338 Order of pole (three term test) = -0.4396 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = -14.231089627644117810351467138762 y[1] (numeric) = -14.231089627644117810351467138759 absolute error = 3e-30 relative error = 2.1080606464402081438965302351453e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = -14.218426675263773975715043244917 bytes used=304089232, alloc=4586680, time=10.40 y[1] (numeric) = -14.218426675263773975715043244912 absolute error = 5e-30 relative error = 3.5165634807532192776756287906831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = -14.205758286036730234024437412528 y[1] (numeric) = -14.205758286036730234024437412524 absolute error = 4e-30 relative error = 2.8157595810508201189332450628660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1322 Order of pole (three term test) = 8.295 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = -14.193084459086242165018930888271 y[1] (numeric) = -14.193084459086242165018930888267 absolute error = 4e-30 relative error = 2.8182739358246036880120606551153e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02571 Order of pole (three term test) = -15.62 Radius of convergence (six term test) for eq 1 = 0.3418 Order of pole (six term test) = -11.56 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = -14.180405193535478923803547487485 y[1] (numeric) = -14.18040519353547892380354748748 absolute error = 5e-30 relative error = 3.5259923336177905378316918837703e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04475 Order of pole (three term test) = 0.4841 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = -14.167720488507523234725208071583 y[1] (numeric) = -14.167720488507523234725208071579 absolute error = 4e-30 relative error = 2.8233193923078121506594710313341e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03272 Order of pole (three term test) = -25.58 Radius of convergence (six term test) for eq 1 = 1.685 Order of pole (six term test) = -14.9 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = -14.155030343125371385248546550095 y[1] (numeric) = -14.15503034312537138524854655009 absolute error = 5e-30 relative error = 3.5323131627395868596518248629673e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=308090164, alloc=4586680, time=10.53 x[1] = 3.17 y[1] (analytic) = -14.142334756511933219831387391972 y[1] (numeric) = -14.142334756511933219831387391967 absolute error = 5e-30 relative error = 3.5354841234384699802410329672327e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = -14.129633727790032133799884630882 y[1] (numeric) = -14.129633727790032133799884630877 absolute error = 5e-30 relative error = 3.5386621453364686496040091022897e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.292 Order of pole (six term test) = -12.54 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = -14.116927256082405067223322349115 y[1] (numeric) = -14.116927256082405067223322349111 absolute error = 4e-30 relative error = 2.8334778011104109263339328632231e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = -14.104215340511702498788576624799 y[1] (numeric) = -14.104215340511702498788576624794 absolute error = 5e-30 relative error = 3.5450394646474530108553901552383e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7156 Order of pole (six term test) = -9.292 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = -14.091497980200488439674238927058 y[1] (numeric) = -14.091497980200488439674238927054 absolute error = 4e-30 relative error = 2.8385910466156767891181117811858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = -14.078775174271240427424400943828 y[1] (numeric) = -14.078775174271240427424400943823 absolute error = 5e-30 relative error = 3.5514453055102607505676910159261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=312091060, alloc=4586680, time=10.67 x[1] = 3.23 y[1] (analytic) = -14.066046921846349519822100826942 y[1] (numeric) = -14.066046921846349519822100826936 absolute error = 6e-30 relative error = 4.2655907756721906711498491253838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3059 Order of pole (three term test) = -65.78 Radius of convergence (six term test) for eq 1 = 1.394 Order of pole (six term test) = -12.23 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = -14.053313222048120288762430839189 y[1] (numeric) = -14.053313222048120288762430839184 absolute error = 5e-30 relative error = 3.5578798543787835738046469302719e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = -14.040574073998770814125306388005 y[1] (numeric) = -14.040574073998770814125306388 absolute error = 5e-30 relative error = 3.5611079530283013172751928797447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03064 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = -14.027829476820432677647896430434 y[1] (numeric) = -14.027829476820432677647896430428 absolute error = 6e-30 relative error = 4.2772119592089369606647338950342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = -14.015079429635150956796715234053 y[1] (numeric) = -14.015079429635150956796715234048 absolute error = 5e-30 relative error = 3.5675859170854253452057767363361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2998 Order of pole (six term test) = -11.84 TOP MAIN SOLVE Loop bytes used=316091888, alloc=4586680, time=10.80 x[1] = 3.28 y[1] (analytic) = -14.002323931564884218639375478523 y[1] (numeric) = -14.002323931564884218639375478517 absolute error = 6e-30 relative error = 4.2850029961629709586701531443317e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.885 Order of pole (six term test) = -10.88 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = -13.98956298173150451371600268239 y[1] (numeric) = -13.989562981731504513716002682384 absolute error = 6e-30 relative error = 4.2889116749645406061047402755786e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3139 Order of pole (six term test) = -11.61 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = -13.976796579256797369910310939854 y[1] (numeric) = -13.976796579256797369910310939849 absolute error = 5e-30 relative error = 3.5773576381733890560394705971199e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.106 Order of pole (three term test) = -22.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = -13.964024723262461786320339952126 y[1] (numeric) = -13.964024723262461786320339952119 absolute error = 7e-30 relative error = 5.0128814140086731347064840080918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.434 Order of pole (six term test) = -10.65 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = -13.951247412870110227128853338034 y[1] (numeric) = -13.951247412870110227128853338029 absolute error = 5e-30 relative error = 3.5839089165514115390135931610924e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9792 Order of pole (six term test) = -13.27 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = -13.938464647201268615473398208583 y[1] (numeric) = -13.938464647201268615473398208578 absolute error = 5e-30 relative error = 3.5871956679274282263410094652256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.347 Order of pole (six term test) = -12.1 TOP MAIN SOLVE Loop bytes used=320093344, alloc=4586680, time=10.93 x[1] = 3.34 y[1] (analytic) = -13.925676425377376327316025990059 y[1] (numeric) = -13.925676425377376327316025990052 absolute error = 7e-30 relative error = 5.0266858041047042188958057626629e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.541 Order of pole (six term test) = -15.48 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = -13.912882746519786185312674480386 y[1] (numeric) = -13.91288274651978618531267448038 absolute error = 6e-30 relative error = 4.3125498211367155713324294536022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08453 Order of pole (three term test) = -23.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = -13.900083609749764452682211123396 y[1] (numeric) = -13.900083609749764452682211123391 absolute error = 5e-30 relative error = 3.5971006652743524363399214162301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05768 Order of pole (three term test) = -27.67 Radius of convergence (six term test) for eq 1 = 0.5735 Order of pole (six term test) = -11.09 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = -13.887279014188490827075137485632 y[1] (numeric) = -13.887279014188490827075137485626 absolute error = 6e-30 relative error = 4.3205007934742734068653347239519e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04439 Order of pole (three term test) = -2.331 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = -13.874468958957058434441954920362 y[1] (numeric) = -13.874468958957058434441954920357 absolute error = 5e-30 relative error = 3.6037415304260042709129418269529e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.249 Order of pole (six term test) = -11.19 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = -13.861653443176473822901191403483 y[1] (numeric) = -13.861653443176473822901191403478 absolute error = 5e-30 relative error = 3.6070732979270203203009055778469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.568 Order of pole (six term test) = -13.3 bytes used=324094616, alloc=4586680, time=11.07 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = -13.848832465967656956607089525927 y[1] (numeric) = -13.848832465967656956607089525921 absolute error = 6e-30 relative error = 4.3324951866841455716273159142252e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = -13.836006026451441209616955627251 y[1] (numeric) = -13.836006026451441209616955627246 absolute error = 5e-30 relative error = 3.6137596286392799798844322274488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.775 Order of pole (six term test) = -8.609 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = -13.823174123748573359758170055075 y[1] (numeric) = -13.823174123748573359758170055068 absolute error = 7e-30 relative error = 5.0639599395437098549507279038343e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = -13.810336756979713582494858534978 y[1] (numeric) = -13.810336756979713582494858534972 absolute error = 6e-30 relative error = 4.3445718273072619323941537452857e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9409 Order of pole (six term test) = -11.21 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = -13.797493925265435444794224635572 y[1] (numeric) = -13.797493925265435444794224635567 absolute error = 5e-30 relative error = 3.6238464949378916065549323173324e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=328095596, alloc=4586680, time=11.20 x[1] = 3.45 y[1] (analytic) = -13.784645627726225898992543313339 y[1] (numeric) = -13.784645627726225898992543313334 absolute error = 5e-30 relative error = 3.6272241848155140720858270213150e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = -13.771791863482485276660815521927 y[1] (numeric) = -13.771791863482485276660815521922 absolute error = 5e-30 relative error = 3.6306096182429855180199956023313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = -13.758932631654527282470083870545 y[1] (numeric) = -13.758932631654527282470083870541 absolute error = 4e-30 relative error = 2.9072022569522498308950510206909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9112 Order of pole (six term test) = -11.96 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = -13.746067931362578988056409316106 y[1] (numeric) = -13.746067931362578988056409316102 absolute error = 4e-30 relative error = 2.9099230557952727931348483371599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1558 Order of pole (three term test) = -34.79 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = -12.62 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = -13.733197761726780825885508873764 y[1] (numeric) = -13.733197761726780825885508873759 absolute error = 5e-30 relative error = 3.6408126401081633111514754570757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004128 Order of pole (three term test) = -25.48 Radius of convergence (six term test) for eq 1 = 5.998 Order of pole (six term test) = -45.44 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = -13.720322121867186583117054330502 y[1] (numeric) = -13.720322121867186583117054330498 absolute error = 4e-30 relative error = 2.9153834468834201935878256473362e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=332096676, alloc=4586680, time=11.34 x[1] = 3.51 y[1] (analytic) = -13.707441010903763395468631946431 y[1] (numeric) = -13.707441010903763395468631946426 absolute error = 5e-30 relative error = 3.6476538516727407728977715473470e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = -13.694554427956391741079363128412 y[1] (numeric) = -13.694554427956391741079363128407 absolute error = 5e-30 relative error = 3.6510862958731100613310165000242e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.015 Order of pole (six term test) = -11.18 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = -13.681662372144865434373186060697 y[1] (numeric) = -13.681662372144865434373186060693 absolute error = 4e-30 relative error = 2.9236213343078737044471466992190e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.335 Order of pole (six term test) = -12.95 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = -13.668764842588891619921798277202 y[1] (numeric) = -13.668764842588891619921798277197 absolute error = 5e-30 relative error = 3.6579749945079821265572960867449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.325 Order of pole (six term test) = -12.04 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = -13.655861838408090766307260160063 y[1] (numeric) = -13.655861838408090766307260160059 absolute error = 4e-30 relative error = 2.9291450421310745363687545200219e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=336097812, alloc=4586680, time=11.48 x[1] = 3.56 y[1] (analytic) = -13.642953358721996659984259349149 y[1] (numeric) = -13.642953358721996659984259349144 absolute error = 5e-30 relative error = 3.6648956193956928430338599411119e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = -13.63003940265005639914203604713 y[1] (numeric) = -13.630039402650056399142036047126 absolute error = 4e-30 relative error = 2.9346943774955554703232735514247e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1118 Order of pole (three term test) = -28.87 Radius of convergence (six term test) for eq 1 = 0.9624 Order of pole (six term test) = -11.56 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = -13.617119969311630387565969204799 y[1] (numeric) = -13.617119969311630387565969204795 absolute error = 4e-30 relative error = 2.9374787098994818565196736755281e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.38 Order of pole (three term test) = -124.4 Radius of convergence (six term test) for eq 1 = 1.343 Order of pole (six term test) = -12.17 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = -13.604195057825992328498823571244 y[1] (numeric) = -13.60419505782599232849882357124 absolute error = 4e-30 relative error = 2.9402695146589708249265313972418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6656 Order of pole (six term test) = -11.57 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = -13.591264667312329218501657593551 y[1] (numeric) = -13.591264667312329218501657593546 absolute error = 5e-30 relative error = 3.6788335172555721670251734837759e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08331 Order of pole (three term test) = -25.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = -13.578328796889741341314392150653 y[1] (numeric) = -13.578328796889741341314392150648 absolute error = 5e-30 relative error = 3.6823382868334300860966927949575e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1716 Order of pole (six term test) = -11.42 TOP MAIN SOLVE Loop bytes used=340098828, alloc=4586680, time=11.62 x[1] = 3.62 y[1] (analytic) = -13.565387445677242261716040105997 y[1] (numeric) = -13.565387445677242261716040105992 absolute error = 5e-30 relative error = 3.6858512298469618666132831236775e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.087 Order of pole (six term test) = -11.95 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = -13.552440612793758819384596663641 y[1] (numeric) = -13.552440612793758819384596663636 absolute error = 5e-30 relative error = 3.6893723742127347637607012369401e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09589 Order of pole (three term test) = 4.975 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = -13.539488297358131122756590512443 y[1] (numeric) = -13.539488297358131122756590512437 absolute error = 6e-30 relative error = 4.4314820975699203221462449668010e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.279 Order of pole (three term test) = -94.2 Radius of convergence (six term test) for eq 1 = 2.826 Order of pole (six term test) = -14.77 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = -13.526530498489112542886295742975 y[1] (numeric) = -13.526530498489112542886295742969 absolute error = 6e-30 relative error = 4.4357272551673087694593736603881e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = -13.51356721530536970730460452181 y[1] (numeric) = -13.513567215305369707304604521804 absolute error = 6e-30 relative error = 4.4399823558093845532087272626779e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1518 Order of pole (three term test) = 2.678 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = -13.50059844692548249387756050781 y[1] (numeric) = -13.500598446925482493877560507803 absolute error = 7e-30 relative error = 5.1849553392161838543448545332788e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=344099856, alloc=4586680, time=11.75 x[1] = 3.68 y[1] (analytic) = -13.48762419246794402466455299506 y[1] (numeric) = -13.487624192467944024664552995053 absolute error = 7e-30 relative error = 5.1899429433310382979062082876574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.425 Order of pole (six term test) = -11.55 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = -13.474644451051160659776171767094 y[1] (numeric) = -13.474644451051160659776171767088 absolute error = 6e-30 relative error = 4.4528076579652818790626289298840e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6207 Order of pole (six term test) = -12.55 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = -13.461659221793451991231722647041 y[1] (numeric) = -13.461659221793451991231722647035 absolute error = 6e-30 relative error = 4.4571028735346637289437062760396e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1104 Order of pole (three term test) = -20 Radius of convergence (six term test) for eq 1 = 1.157 Order of pole (six term test) = -11.32 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = -13.448668503813050836816403728329 y[1] (numeric) = -13.448668503813050836816403728323 absolute error = 6e-30 relative error = 4.4614082043131945525435476689751e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03944 Order of pole (three term test) = -25.6 Radius of convergence (six term test) for eq 1 = 0.6724 Order of pole (six term test) = -11.36 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = -13.435672296228103233938142270589 y[1] (numeric) = -13.435672296228103233938142270584 absolute error = 5e-30 relative error = 3.7214364043425555964657275406013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1015 Order of pole (three term test) = -25.38 Radius of convergence (six term test) for eq 1 = 0.4979 Order of pole (six term test) = -11.54 TOP MAIN SOLVE Loop bytes used=348100680, alloc=4586680, time=11.89 x[1] = 3.73 y[1] (analytic) = -13.4226705981566684334840922454 y[1] (numeric) = -13.422670598156668433484092245395 absolute error = 5e-30 relative error = 3.7250411260830974943450476355675e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03859 Order of pole (three term test) = -0.8814 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = -13.40966340871671889367679251649 y[1] (numeric) = -13.409663408716718893676792516484 absolute error = 6e-30 relative error = 4.4743852378127583470864004591393e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05008 Order of pole (three term test) = -5.915 Radius of convergence (six term test) for eq 1 = 1.558 Order of pole (six term test) = -10.75 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = -13.396650727026140273929985639053 y[1] (numeric) = -13.396650727026140273929985639047 absolute error = 6e-30 relative error = 4.4787313801469181749209409625960e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.529 Order of pole (six term test) = -10.42 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = -13.383632552202731428704097262807 y[1] (numeric) = -13.383632552202731428704097262801 absolute error = 6e-30 relative error = 4.4830878138629830788924090139958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = -13.370608883364204401361376123416 y[1] (numeric) = -13.370608883364204401361376123411 absolute error = 5e-30 relative error = 3.7395454789056251745488692116781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06716 Order of pole (three term test) = -21.31 Radius of convergence (six term test) for eq 1 = 0.6192 Order of pole (six term test) = -11.63 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = -13.357579719628184418020694606929 y[1] (numeric) = -13.357579719628184418020694606925 absolute error = 4e-30 relative error = 2.9945544656733234912277247983492e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=352101988, alloc=4586680, time=12.03 x[1] = 3.79 y[1] (analytic) = -13.344545060112209881412009871857 y[1] (numeric) = -13.344545060112209881412009871851 absolute error = 6e-30 relative error = 4.4962192213913870042689393192831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2673 Order of pole (three term test) = -42.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = -13.331504903933732364730485513506 y[1] (numeric) = -13.331504903933732364730485513502 absolute error = 4e-30 relative error = 3.0004114530383726116077810857516e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07487 Order of pole (three term test) = 1.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = -13.318459250210116605490273755254 y[1] (numeric) = -13.318459250210116605490273755248 absolute error = 6e-30 relative error = 4.5050256094039871249600649060665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = -13.305408098058640499377958151307 y[1] (numeric) = -13.305408098058640499377958151302 absolute error = 5e-30 relative error = 3.7578704562466879548280367808029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.284 Order of pole (six term test) = -12.77 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = -13.292351446596495094105656785677 y[1] (numeric) = -13.292351446596495094105656785672 absolute error = 5e-30 relative error = 3.7615616921415731655987828547940e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.059 Order of pole (six term test) = -15.11 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = -13.27928929494078458326378595191 y[1] (numeric) = -13.279289294940784583263785951906 bytes used=356103232, alloc=4586680, time=12.16 absolute error = 4e-30 relative error = 3.0122093970224307275129232185869e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = -13.266221642208526300173484298269 y[1] (numeric) = -13.266221642208526300173484298265 absolute error = 4e-30 relative error = 3.0151765196454914164013152842052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09486 Order of pole (three term test) = -29.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = -13.253148487516650711738697422952 y[1] (numeric) = -13.253148487516650711738697422947 absolute error = 5e-30 relative error = 3.7726884330237292266979743824008e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = -13.240069829982001412297922903997 y[1] (numeric) = -13.240069829982001412297922903993 absolute error = 4e-30 relative error = 3.0211321022960477929067490400825e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.719 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = -13.226985668721335117475615748503 y[1] (numeric) = -13.226985668721335117475615748499 absolute error = 4e-30 relative error = 3.0241206123471090770091070337371e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05413 Order of pole (three term test) = 0.3118 Radius of convergence (six term test) for eq 1 = 1.341 Order of pole (six term test) = -9.26 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = -13.213896002851321658033254245775 y[1] (numeric) = -13.213896002851321658033254245771 absolute error = 4e-30 relative error = 3.0271163017605646152659725876982e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.804 Order of pole (six term test) = -11.15 TOP MAIN SOLVE Loop bytes used=360104096, alloc=4586680, time=12.30 x[1] = 3.9 y[1] (analytic) = -13.200800831488543973720066209037 y[1] (numeric) = -13.200800831488543973720066209033 absolute error = 4e-30 relative error = 3.0301191958434793180175339231698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0539 Order of pole (three term test) = -28.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = -13.187700153749498107123415590334 y[1] (numeric) = -13.18770015374949810712341559033 absolute error = 4e-30 relative error = 3.0331293200222851105631112893130e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = -13.174593968750593197518849453245 y[1] (numeric) = -13.17459396875059319751884945324 absolute error = 5e-30 relative error = 3.7951833748043567163644386117262e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = -13.16148227560815147471980528803 y[1] (numeric) = -13.161482275608151474719805288024 absolute error = 6e-30 relative error = 4.5587570414615465629494124679156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07444 Order of pole (three term test) = -23.12 Radius of convergence (six term test) for eq 1 = 1.07 Order of pole (six term test) = -11.65 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = -13.148365073438408252926978653846 y[1] (numeric) = -13.14836507343840825292697865384 absolute error = 6e-30 relative error = 4.5633049938055526205948351163085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.106 Order of pole (three term test) = -446.2 Radius of convergence (six term test) for eq 1 = 1.536 Order of pole (six term test) = -12.06 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = -13.135242361357511924577351132644 y[1] (numeric) = -13.135242361357511924577351132639 absolute error = 5e-30 relative error = 3.8065532880531150336482083566330e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05336 Order of pole (three term test) = -32.29 Radius of convergence (six term test) for eq 1 = 0.6178 Order of pole (six term test) = -12.05 TOP MAIN SOLVE Loop bytes used=364105464, alloc=4586680, time=12.44 x[1] = 3.96 y[1] (analytic) = -13.122114138481523954192878579374 y[1] (numeric) = -13.122114138481523954192878579369 absolute error = 5e-30 relative error = 3.8103616134058366631323737528974e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08588 Order of pole (three term test) = -0.1142 Radius of convergence (six term test) for eq 1 = 4.643 Order of pole (six term test) = -14.54 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = -13.108980403926418872228839653117 y[1] (numeric) = -13.108980403926418872228839653112 absolute error = 5e-30 relative error = 3.8141791702597964769121020679781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2529 Order of pole (three term test) = -17.12 Radius of convergence (six term test) for eq 1 = 1.124 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = -13.095841156808084268921844613775 y[1] (numeric) = -13.095841156808084268921844613769 absolute error = 6e-30 relative error = 4.5816071897610053222895788618467e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03692 Order of pole (three term test) = -12 Radius of convergence (six term test) for eq 1 = 1.834 Order of pole (six term test) = -11.2 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = -13.082696396242320788137504368922 y[1] (numeric) = -13.082696396242320788137504368916 absolute error = 6e-30 relative error = 4.5862105320454816927106970402732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = -13.069546121344842121217759755467 y[1] (numeric) = -13.069546121344842121217759755461 absolute error = 6e-30 relative error = 4.5908250709647493920335233467571e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01876 Order of pole (three term test) = -0.7626 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=368106784, alloc=4586680, time=12.57 x[1] = 4.01 y[1] (analytic) = -13.056390331231275000827871040709 y[1] (numeric) = -13.056390331231275000827871040703 absolute error = 6e-30 relative error = 4.5954508465083347623202537512294e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1068 Order of pole (three term test) = -3.705 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = -13.043229025017159194803067627439 y[1] (numeric) = -13.043229025017159194803067627433 absolute error = 6e-30 relative error = 4.6000878988568604234588513697295e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02123 Order of pole (three term test) = -1.319 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = -13.030062201817947499994857947682 y[1] (numeric) = -13.030062201817947499994857947678 absolute error = 4e-30 relative error = 3.0698241789221252380901723496962e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = -13.016889860749005736116999529723 y[1] (numeric) = -13.016889860749005736116999529718 absolute error = 5e-30 relative error = 3.8411633297113068322976466865018e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00728 Order of pole (three term test) = -0.885 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = -13.003712000925612739591129222994 y[1] (numeric) = -13.003712000925612739591129222989 absolute error = 5e-30 relative error = 3.8450559345240010885018146944726e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001769 Order of pole (three term test) = -0.8946 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = -12.990528621462960357392053565493 y[1] (numeric) = -12.990528621462960357392053565488 absolute error = 5e-30 relative error = 3.8489580722211693124368243471891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2071 Order of pole (three term test) = -12.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=372107500, alloc=4652204, time=12.71 x[1] = 4.07 y[1] (analytic) = -12.977339721476153440892699278303 y[1] (numeric) = -12.977339721476153440892699278298 absolute error = 5e-30 relative error = 3.8528697770973181413506455190079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.225 Order of pole (six term test) = -12.59 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = -12.964145300080209839708723871855 y[1] (numeric) = -12.964145300080209839708723871848 absolute error = 7e-30 relative error = 5.3995075170568249005625401658585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.086 Order of pole (six term test) = -11.36 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = -12.950945356390060395542786348529 y[1] (numeric) = -12.950945356390060395542786348523 absolute error = 6e-30 relative error = 4.6328664316690753155831833871457e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = -12.937739889520548936028477986247 y[1] (numeric) = -12.93773988952054893602847798624 absolute error = 7e-30 relative error = 5.4105276963172957452808023174249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1462 Order of pole (three term test) = -14.87 Radius of convergence (six term test) for eq 1 = 1.729 Order of pole (six term test) = -11.18 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = -12.924528898586432268573913187608 y[1] (numeric) = -12.924528898586432268573913187602 absolute error = 6e-30 relative error = 4.6423355520960037262863034210075e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1517 Order of pole (three term test) = -25.93 Radius of convergence (six term test) for eq 1 = 0.523 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = -12.911312382702380174204980379252 y[1] (numeric) = -12.911312382702380174204980379245 absolute error = 7e-30 relative error = 5.4216022295131526840603121116028e-29 % bytes used=376109036, alloc=4652204, time=12.85 Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.967 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7349 Order of pole (six term test) = -12.36 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = -12.898090340982975401408252945994 y[1] (numeric) = -12.898090340982975401408252945987 absolute error = 7e-30 relative error = 5.4271600019406621103404027502500e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = -12.884862772542713659973560184407 y[1] (numeric) = -12.8848627725427136599735601844 absolute error = 7e-30 relative error = 5.4327315110540458923237780770435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7248 Order of pole (six term test) = -11.68 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = -12.871629676496003614836218260409 y[1] (numeric) = -12.871629676496003614836218260403 absolute error = 6e-30 relative error = 4.6614144057890250947333905557913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01477 Order of pole (three term test) = 0.3273 Radius of convergence (six term test) for eq 1 = 1.587 Order of pole (six term test) = -14.58 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = -12.858391051957166879918921155508 y[1] (numeric) = -12.858391051957166879918921155501 absolute error = 7e-30 relative error = 5.4439159391831801558693435412139e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1233 Order of pole (three term test) = -1.887 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = -12.84514689804043801197329158628 y[1] (numeric) = -12.845146898040438011973291586273 absolute error = 7e-30 relative error = 5.4495289587290504089272981569933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=380109828, alloc=4652204, time=12.99 x[1] = 4.18 y[1] (analytic) = -12.831897213859964504421091881723 y[1] (numeric) = -12.831897213859964504421091881715 absolute error = 8e-30 relative error = 6.2344639040274225066333432969343e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.335 Order of pole (six term test) = -13.04 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = -12.818641998529806781195094803066 y[1] (numeric) = -12.81864199852980678119509480306 absolute error = 6e-30 relative error = 4.6806830245264286530534193215726e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.083 Order of pole (six term test) = -5.793 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = -12.805381251163938190579614290675 y[1] (numeric) = -12.805381251163938190579614290669 absolute error = 6e-30 relative error = 4.6855301551093086361138878092084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02228 Order of pole (three term test) = -25.65 Radius of convergence (six term test) for eq 1 = 0.5509 Order of pole (six term test) = -12.1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = -12.792114970876244999050696122617 y[1] (numeric) = -12.792114970876244999050696122611 absolute error = 6e-30 relative error = 4.6903893638074509719922525784292e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = -12.778843156780526385115968469543 y[1] (numeric) = -12.778843156780526385115968469537 absolute error = 6e-30 relative error = 4.6952606948746891046553172585362e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.595 Order of pole (six term test) = -7.626 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = -12.765565807990494433154152330457 y[1] (numeric) = -12.765565807990494433154152330451 absolute error = 6e-30 relative error = 4.7001441927817663978948335085088e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=384110788, alloc=4652204, time=13.13 x[1] = 4.24 y[1] (analytic) = -12.752282923619774127254231833997 y[1] (numeric) = -12.752282923619774127254231833991 absolute error = 6e-30 relative error = 4.7050399022176664736555037200333e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = -12.738994502781903345054284389824 y[1] (numeric) = -12.738994502781903345054284389819 absolute error = 5e-30 relative error = 3.9249565567424611279646444005305e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.258 Order of pole (six term test) = -12.74 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = -12.725700544590332851579970674735 y[1] (numeric) = -12.725700544590332851579970674731 absolute error = 4e-30 relative error = 3.1432454236874143253310641158582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.423 Order of pole (six term test) = -10.22 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = -12.712401048158426293082684438092 y[1] (numeric) = -12.712401048158426293082684438086 absolute error = 6e-30 relative error = 4.7198007498899557580340789826229e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4726 Order of pole (three term test) = -21.87 Radius of convergence (six term test) for eq 1 = 0.245 Order of pole (six term test) = -11.68 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = -12.699096012599460190877362111169 y[1] (numeric) = -12.699096012599460190877362111164 absolute error = 5e-30 relative error = 3.9372881306190846134442086217875e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = -35.99 Radius of convergence (six term test) for eq 1 = 0.7502 Order of pole (six term test) = -11.86 TOP MAIN SOLVE Loop bytes used=388111496, alloc=4652204, time=13.26 x[1] = 4.29 y[1] (analytic) = -12.685785437026623935179952205052 y[1] (numeric) = -12.685785437026623935179952205048 absolute error = 4e-30 relative error = 3.1531354679269632617615195965647e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2634 Order of pole (three term test) = -9.082 Radius of convergence (six term test) for eq 1 = 1.395 Order of pole (six term test) = -12.22 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = -12.672469320553019778944544481648 y[1] (numeric) = -12.672469320553019778944544481643 absolute error = 5e-30 relative error = 3.9455609427995858631599941811448e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = -12.65914766229166283170015888243 y[1] (numeric) = -12.659147662291662831700158882426 absolute error = 4e-30 relative error = 3.1597703942698833825550899341912e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0706 Order of pole (three term test) = -23.61 Radius of convergence (six term test) for eq 1 = 0.2879 Order of pole (six term test) = -11.99 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = -12.645820461355481053387194199534 y[1] (numeric) = -12.64582046135548105338719419953 absolute error = 4e-30 relative error = 3.1631004190069354592177251087316e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6059 Order of pole (six term test) = -11.12 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = -12.632487716857315248193536473774 y[1] (numeric) = -12.632487716857315248193536473768 absolute error = 6e-30 relative error = 4.7496582893908943124909631660856e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.932 Order of pole (six term test) = -14.4 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = -12.619149427909919058390327104198 y[1] (numeric) = -12.619149427909919058390327104192 absolute error = 6e-30 relative error = 4.7546786209930523953876770907279e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7883 Order of pole (six term test) = -11.94 TOP MAIN SOLVE Loop bytes used=392112328, alloc=4652204, time=13.40 x[1] = 4.35 y[1] (analytic) = -12.605805593625958958167390653792 y[1] (numeric) = -12.605805593625958958167390653787 absolute error = 5e-30 relative error = 3.9664263920809761347209878409632e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = -12.592456213118014247468322335908 y[1] (numeric) = -12.592456213118014247468322335903 absolute error = 5e-30 relative error = 3.9706312377654490353954981247447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3373 Order of pole (three term test) = -41.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = -12.579101285498577045825235166024 y[1] (numeric) = -12.579101285498577045825235166019 absolute error = 5e-30 relative error = 3.9748467609240839850929354696510e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = -12.565740809880052286193166763446 y[1] (numeric) = -12.565740809880052286193166763442 absolute error = 4e-30 relative error = 3.1832584011719580079160467389417e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6719 Order of pole (three term test) = 69.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = -12.552374785374757708784145787539 y[1] (numeric) = -12.552374785374757708784145787534 absolute error = 5e-30 relative error = 3.9833099994956232396475599116770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05364 Order of pole (three term test) = -3.562 Radius of convergence (six term test) for eq 1 = 1.927 Order of pole (six term test) = -10.53 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = -12.53900321109492385490091799307 y[1] (numeric) = -12.539003211094923854900917993065 absolute error = 5e-30 relative error = 3.9875577953244600730190846191008e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.754 Order of pole (three term test) = 97.72 Radius of convergence (six term test) for eq 1 = 1.926 Order of pole (six term test) = -11.77 bytes used=396116248, alloc=4652204, time=13.54 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = -12.525626086152694060770331889296 y[1] (numeric) = -12.525626086152694060770331889291 absolute error = 5e-30 relative error = 3.9918164294618297245836966390579e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0984 Order of pole (three term test) = -22.21 Radius of convergence (six term test) for eq 1 = 0.5341 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = -12.512243409660124451376383987353 y[1] (numeric) = -12.512243409660124451376383987348 absolute error = 5e-30 relative error = 3.9960859426213937363048443072434e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04381 Order of pole (three term test) = -35.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = -12.498855180729183934292923620568 y[1] (numeric) = -12.498855180729183934292923620562 absolute error = 6e-30 relative error = 4.8004396508656560439518615382125e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5382 Order of pole (three term test) = -61 Radius of convergence (six term test) for eq 1 = 3.648 Order of pole (six term test) = -5.677 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = -12.485461398471754193516017322268 y[1] (numeric) = -12.485461398471754193516017322262 absolute error = 6e-30 relative error = 4.8055893238630429574575348178303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.195 Order of pole (six term test) = -13.47 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = -12.472062061999629683295972745709 y[1] (numeric) = -12.472062061999629683295972745703 absolute error = 6e-30 relative error = 4.8107521997353080122845284990513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=400117204, alloc=4652204, time=13.67 x[1] = 4.46 y[1] (analytic) = -12.458657170424517621969022110681 y[1] (numeric) = -12.458657170424517621969022110676 absolute error = 5e-30 relative error = 4.0132736069417258579296839734630e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00441 Order of pole (three term test) = -0.8822 Radius of convergence (six term test) for eq 1 = 2.679 Order of pole (six term test) = -15.56 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = -12.445246722858037985788665161417 y[1] (numeric) = -12.445246722858037985788665161412 absolute error = 5e-30 relative error = 4.0175981331222296510569331107016e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2641 Order of pole (three term test) = -21.2 Radius of convergence (six term test) for eq 1 = 1.028 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = -12.431830718411723502756671620366 y[1] (numeric) = -12.431830718411723502756671620361 absolute error = 5e-30 relative error = 4.0219337869481497337568800334450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6463 Order of pole (six term test) = -12.09 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = -12.41840915619701964645374312245 y[1] (numeric) = -12.418409156197019646453743122445 absolute error = 5e-30 relative error = 4.0262806105924654571413214168748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04203 Order of pole (three term test) = -29.84 Radius of convergence (six term test) for eq 1 = 1.292 Order of pole (six term test) = -10.11 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = -12.404982035325284629869834614379 y[1] (numeric) = -12.404982035325284629869834614375 absolute error = 4e-30 relative error = 3.2245109171535463783364090716400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.476 Order of pole (six term test) = -11.64 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = -12.391549354907789399234135203621 y[1] (numeric) = -12.391549354907789399234135203616 absolute error = 5e-30 relative error = 4.0350079370984412712267230493404e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1257 Order of pole (three term test) = -19.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=404118280, alloc=4652204, time=13.81 x[1] = 4.52 y[1] (analytic) = -12.378111114055717627844708441606 y[1] (numeric) = -12.3781111140557176278447084416 absolute error = 6e-30 relative error = 4.8472662304564542644731024296064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.545 Order of pole (six term test) = -17.48 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = -12.364667311880165709897792025771 y[1] (numeric) = -12.364667311880165709897792025765 absolute error = 6e-30 relative error = 4.8525365451888108408563481447607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06454 Order of pole (three term test) = 4.561 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = -12.351217947492142754316756905024 y[1] (numeric) = -12.35121794749214275431675690502 absolute error = 4e-30 relative error = 3.2385470137478882067588703612560e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03089 Order of pole (three term test) = -28.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = -12.337763020002570578580725773216 y[1] (numeric) = -12.337763020002570578580725773211 absolute error = 5e-30 relative error = 4.0525985074391210406860688557258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = -12.324302528522283702552850935196 y[1] (numeric) = -12.324302528522283702552850935191 absolute error = 5e-30 relative error = 4.0570247187850501058817001784777e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.207 Order of pole (three term test) = -56.58 Radius of convergence (six term test) for eq 1 = 4.025 Order of pole (six term test) = -14.03 TOP MAIN SOLVE Loop bytes used=408119336, alloc=4652204, time=13.95 x[1] = 4.57 y[1] (analytic) = -12.310836472162029342308251530069 y[1] (numeric) = -12.310836472162029342308251530065 absolute error = 4e-30 relative error = 3.2491699561155164314136843963271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.106 Order of pole (six term test) = -13.31 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = -12.297364850032467403961610096211 y[1] (numeric) = -12.297364850032467403961610096206 absolute error = 5e-30 relative error = 4.0659117306638251365997560332008e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01508 Order of pole (three term test) = -26.3 Radius of convergence (six term test) for eq 1 = 1.315 Order of pole (six term test) = -11.43 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = -12.283887661244170477494428462634 y[1] (numeric) = -12.283887661244170477494428462629 absolute error = 5e-30 relative error = 4.0703726197163677540622541846013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.212 Order of pole (six term test) = 6.922 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = -12.270404904907623830581942951301 y[1] (numeric) = -12.270404904907623830581942951296 absolute error = 5e-30 relative error = 4.0748451569028657564553619254753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.465 Order of pole (six term test) = -11.41 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = -12.256916580133225402419698874957 y[1] (numeric) = -12.256916580133225402419698874953 absolute error = 4e-30 relative error = 3.2634635096427509308092102285807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03177 Order of pole (three term test) = -0.3235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = -12.243422686031285797549784315071 y[1] (numeric) = -12.243422686031285797549784315067 absolute error = 4e-30 relative error = 3.2670602841831664761464484362061e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.767 Order of pole (three term test) = -216.2 Radius of convergence (six term test) for eq 1 = 1.644 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop bytes used=412120252, alloc=4652204, time=14.08 x[1] = 4.63 y[1] (analytic) = -12.229923221712028279686723164464 y[1] (numeric) = -12.229923221712028279686723164459 absolute error = 5e-30 relative error = 4.0883331067225341177989458821275e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = -12.216418186285588765543027419214 y[1] (numeric) = -12.216418186285588765543027419209 absolute error = 5e-30 relative error = 4.0928526870610130940349574702213e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07329 Order of pole (three term test) = -13.24 Radius of convergence (six term test) for eq 1 = 2.292 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = -12.202907578862015818654408704418 y[1] (numeric) = -12.202907578862015818654408704414 absolute error = 4e-30 relative error = 3.2779073136051897125651858954511e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5537 Order of pole (three term test) = -96.09 Radius of convergence (six term test) for eq 1 = 1.744 Order of pole (six term test) = -12.05 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = -12.189391398551270643204649018391 y[1] (numeric) = -12.189391398551270643204649018386 absolute error = 5e-30 relative error = 4.1019275175578152994687400495766e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.758 Order of pole (six term test) = -12.7 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = -12.175869644463227077850130679871 y[1] (numeric) = -12.175869644463227077850130679865 absolute error = 6e-30 relative error = 4.9277794319425878319177624507158e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = -12.162342315707671589544025462836 y[1] (numeric) = -12.162342315707671589544025462831 absolute error = 5e-30 relative error = 4.1110502156665146091297109586531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06715 Order of pole (three term test) = -49.38 Radius of convergence (six term test) for eq 1 = 0.9833 Order of pole (six term test) = -11.91 bytes used=416122328, alloc=4652204, time=14.22 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = -12.1488094113943032673601429035 y[1] (numeric) = -12.148809411394303267360142903494 absolute error = 6e-30 relative error = 4.9387555577031541388878720916337e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5838 Order of pole (three term test) = -67.96 Radius of convergence (six term test) for eq 1 = 1.413 Order of pole (six term test) = -11.85 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = -12.135270930632733816316437764046 y[1] (numeric) = -12.135270930632733816316437764042 absolute error = 4e-30 relative error = 3.2961769233374995935127827896610e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.38 Order of pole (six term test) = -12.66 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = -12.121726872532487551198176637726 y[1] (numeric) = -12.121726872532487551198176637721 absolute error = 5e-30 relative error = 4.1248248311301814098942566260635e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6638 Order of pole (six term test) = -12.03 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = -12.108177236203001390380763679835 y[1] (numeric) = -12.10817723620300139038076367983 absolute error = 5e-30 relative error = 4.1294407097462904857025149878435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = -12.094622020753624849652225449213 y[1] (numeric) = -12.094622020753624849652225449208 absolute error = 5e-30 relative error = 4.1340688377200284754100395715536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.979 Order of pole (six term test) = -12.02 TOP MAIN SOLVE Loop bytes used=420123008, alloc=4652204, time=14.36 x[1] = 4.74 y[1] (analytic) = -12.081061225293620036035354844792 y[1] (numeric) = -12.081061225293620036035354844786 absolute error = 6e-30 relative error = 4.9664511156007116787432298412926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2355 Order of pole (three term test) = -44.29 Radius of convergence (six term test) for eq 1 = 2.094 Order of pole (six term test) = -10.96 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = -12.067494848932161641609514121788 y[1] (numeric) = -12.067494848932161641609514121783 absolute error = 5e-30 relative error = 4.1433620337881843730289919852927e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1447 Order of pole (three term test) = -41.54 Radius of convergence (six term test) for eq 1 = 1.604 Order of pole (six term test) = -12.19 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = -12.053922890778336937332096972127 y[1] (numeric) = -12.053922890778336937332096972122 absolute error = 5e-30 relative error = 4.1480271985356492698056014019432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = -12.040345349941145766859649653644 y[1] (numeric) = -12.040345349941145766859649653638 absolute error = 6e-30 relative error = 4.9832457671401663830327700164648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.476 Order of pole (six term test) = -13.95 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = -12.026762225529500540368651152661 y[1] (numeric) = -12.026762225529500540368651152657 absolute error = 4e-30 relative error = 3.3259159239958222189782678968921e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = -12.013173516652226228375952364519 y[1] (numeric) = -12.013173516652226228375952364514 absolute error = 5e-30 relative error = 4.1620975448903497562836131510929e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.107 Order of pole (three term test) = 0.079 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=424124148, alloc=4652204, time=14.49 x[1] = 4.8 y[1] (analytic) = -11.999579222418060355558874276597 y[1] (numeric) = -11.999579222418060355558874276591 absolute error = 6e-30 relative error = 5.0001753301403908947520590495095e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1356 Order of pole (three term test) = -3.435 Radius of convergence (six term test) for eq 1 = 2.07 Order of pole (six term test) = -11.58 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = -11.985979341935652994574965138439 y[1] (numeric) = -11.985979341935652994574965138435 absolute error = 4e-30 relative error = 3.3372325163327267912817552988136e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0491 Order of pole (three term test) = -25.15 Radius of convergence (six term test) for eq 1 = 0.9337 Order of pole (six term test) = -12.14 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = -11.972373874313566759881416603553 y[1] (numeric) = -11.972373874313566759881416603547 absolute error = 6e-30 relative error = 5.0115374469493073601232676421781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.178 Order of pole (six term test) = -17.76 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = -11.958762818660276801554138827396 y[1] (numeric) = -11.95876281866027680155413882739 absolute error = 6e-30 relative error = 5.0172414078132636387758546486737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0747 Order of pole (three term test) = -29.85 Radius of convergence (six term test) for eq 1 = 1.206 Order of pole (six term test) = -11.56 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = -11.945146174084170799106494506214 y[1] (numeric) = -11.94514617408417079910649450621 absolute error = 4e-30 relative error = 3.3486404784884754860267539905455e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.046 Order of pole (six term test) = -11.44 TOP MAIN SOLVE Loop bytes used=428124952, alloc=4652204, time=14.63 x[1] = 4.85 y[1] (analytic) = -11.931523939693548955307691841226 y[1] (numeric) = -11.931523939693548955307691841222 absolute error = 4e-30 relative error = 3.3524636251140410468144407392032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02969 Order of pole (three term test) = -24.47 Radius of convergence (six term test) for eq 1 = 5.356 Order of pole (six term test) = -3.222 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = -11.917896114596623990000836412746 y[1] (numeric) = -11.917896114596623990000836412742 absolute error = 4e-30 relative error = 3.3562970859436669730444093754960e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7048 Order of pole (six term test) = -11.45 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = -11.904262697901521133920641948833 y[1] (numeric) = -11.904262697901521133920641948829 absolute error = 4e-30 relative error = 3.3601409020527734716410933522626e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3024 Order of pole (three term test) = 2.002 Radius of convergence (six term test) for eq 1 = 1.109 Order of pole (six term test) = -12.55 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = -11.890623688716278122510799973012 y[1] (numeric) = -11.890623688716278122510799973006 absolute error = 6e-30 relative error = 5.0459926721032789817292726537925e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7584 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = -11.876979086148845189741008315634 y[1] (numeric) = -11.87697908614884518974100831563 absolute error = 4e-30 relative error = 3.3678597655062596676009767798090e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = -11.863328889307085061923658473478 y[1] (numeric) = -11.863328889307085061923658473473 absolute error = 5e-30 relative error = 4.2146686201262693683886474235490e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=432125788, alloc=4652204, time=14.77 x[1] = 4.91 y[1] (analytic) = -11.849673097298772951530181802096 y[1] (numeric) = -11.849673097298772951530181802091 absolute error = 5e-30 relative error = 4.2195256855986935971805285642678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.289 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = -11.836011709231596551007054525536 y[1] (numeric) = -11.836011709231596551007054525533 absolute error = 3e-30 relative error = 2.5346375736179145984906360252477e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003795 Order of pole (three term test) = -25.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = -11.822344724213156026591461547974 y[1] (numeric) = -11.822344724213156026591461547969 absolute error = 5e-30 relative error = 4.2292794844322037034989140113203e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -29.15 Radius of convergence (six term test) for eq 1 = 2.167 Order of pole (six term test) = -13.59 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = -11.808672141350964012126619051796 y[1] (numeric) = -11.808672141350964012126619051792 absolute error = 4e-30 relative error = 3.3873410592822017439897255864291e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04788 Order of pole (three term test) = -4.734 Radius of convergence (six term test) for eq 1 = 1.012 Order of pole (six term test) = -11.32 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = -11.794993959752445602876755866769 y[1] (numeric) = -11.794993959752445602876755866765 absolute error = 4e-30 relative error = 3.3912692229000110151779700321343e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2006 Order of pole (three term test) = -32.85 Radius of convergence (six term test) for eq 1 = 1.082 Order of pole (six term test) = -12.12 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = -11.781310178524938349341753594776 y[1] (numeric) = -11.781310178524938349341753594773 absolute error = 3e-30 relative error = 2.5464060911225500025004385051016e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=436128504, alloc=4652204, time=14.91 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = -11.767620796775692251071445474747 y[1] (numeric) = -11.767620796775692251071445474742 absolute error = 5e-30 relative error = 4.2489472480027495053650880686218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = -11.753925813611869750479573972297 y[1] (numeric) = -11.753925813611869750479573972293 absolute error = 4e-30 relative error = 3.4031182971800959466079575491530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0482 Order of pole (three term test) = -2.676 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = -11.06 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = -11.740225228140545726657407078693 y[1] (numeric) = -11.740225228140545726657407078689 absolute error = 4e-30 relative error = 3.4070896616295433227372949875541e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06092 Order of pole (three term test) = -8.865 Radius of convergence (six term test) for eq 1 = 1.8 Order of pole (six term test) = -10.5 Finished! diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2)); Iterations = 600 Total Elapsed Time = 14 Seconds Elapsed Time(since restart) = 14 Seconds Time to Timeout = 2 Minutes 45 Seconds Percent Done = 100.2 % > quit bytes used=438326596, alloc=4652204, time=14.98