|\^/| 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_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 2 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 12; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 3; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_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 diff $eq_no = 1 i = 1 order_d = 1 > array_tmp1[1] := array_y_higher[2,1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (2)) * factorial_3(0,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[3,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 order_d = 1 > array_tmp1[2] := array_y_higher[2,2]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (2)) * factorial_3(1,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[3,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 order_d = 1 > array_tmp1[3] := array_y_higher[2,3]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (2)) * factorial_3(2,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 order_d = 1 > array_tmp1[4] := array_y_higher[2,4]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (2)) * factorial_3(3,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[3,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 order_d = 1 > array_tmp1[5] := array_y_higher[2,5]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (2)) * factorial_3(4,6); > array_y[7] := temporary; > array_y_higher[1,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y_higher[2,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[3,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y_higher[2,kkk]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 2; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_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_y_higher[2, 1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 3] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 2)*factorial_3(0, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[3, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y_higher[2, 2]; array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 4] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 2)*factorial_3(1, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[3, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_y_higher[2, 3]; array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 5] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 2)*factorial_3(2, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_y_higher[2, 4]; array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 6] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 2)*factorial_3(3, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[3, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_y_higher[2, 5]; array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 7] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 2)*factorial_3(4, 6); array_y[7] := temporary; array_y_higher[1, 7] := temporary; temporary := temporary*6.0/glob_h; array_y_higher[2, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[3, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y_higher[2, kkk]; array_tmp2[kkk] := array_tmp1[kkk]; order_d := 2; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(1.0 + exp(x)); > end; exact_soln_y := proc(x) return 1.0 + exp(x) end proc > exact_soln_yp := proc(x) > return(exp(x)); > end; exact_soln_yp := proc(x) return exp(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > array_const_1, > #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_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/diffpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"); > 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 := -5.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10000000;"); > 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(1.0 + exp(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_yp := proc(x)"); > omniout_str(ALWAYS,"return(exp(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > 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_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2[1] := 2; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_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_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 := -5.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > array_y_init[1 + 1] := exact_soln_yp(x_start); > glob_look_poles := true; > glob_max_iter := 10000000; > 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] := true; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 2; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 2; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[3,iii] := array_y_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"); > 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,"2013-05-26T00:22:26-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"diff") > ; > logitem_str(html_log_file,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;") > ; > 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,"diff diffeq.mxt") > ; > logitem_str(html_log_file,"diff maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_2, array_const_0D0, array_const_1, 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_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/diffpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"); 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 := -5.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10000000;"); 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(1.0 + exp(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_yp := proc(x)"); omniout_str(ALWAYS, "return(exp(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); 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_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_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_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 := -5.0; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); array_y_init[2] := exact_soln_yp(x_start); glob_look_poles := true; glob_max_iter := 10000000; 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] := true; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 3; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[3, iii] := array_y_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"); 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, "2013-05-26T00:22:26-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "diff"); logitem_str(html_log_file, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"); 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, "diff diffeq.mxt"); logitem_str(html_log_file, "diff 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/diffpostode.ode################# diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -5.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); array_y_init[1 + 1] := exact_soln_yp(x_start); glob_look_poles := true; glob_max_iter := 10000000; 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(1.0 + exp(x)); end; exact_soln_yp := proc(x) return(exp(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 10 estimated_steps = 10000000 step_error = 1.0000000000000000000000000000000e-17 est_needed_step_err = 1.0000000000000000000000000000000e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6707388510135145318336278216148e-185 estimated_step_error = 1.6707388510135145318336278216148e-185 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1212138840850425077445713955376e-177 estimated_step_error = 1.1212138840850425077445713955376e-177 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 = 7.5243392848767301974381056101704e-170 estimated_step_error = 7.5243392848767301974381056101704e-170 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.0494989916234845162087581339859e-162 estimated_step_error = 5.0494989916234845162087581339859e-162 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 = 3.3886619129940291314972567327097e-154 estimated_step_error = 3.3886619129940291314972567327097e-154 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 = 2.2740931884165287534899973804413e-146 estimated_step_error = 2.2740931884165287534899973804413e-146 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 = 1.5261190094150109279521457218486e-138 estimated_step_error = 1.5261190094150109279521457218486e-138 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0241623443297890615626508578016e-130 estimated_step_error = 1.0241623443297890615626508578016e-130 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 = 6.8730534396716051320554906013074e-123 estimated_step_error = 6.8730534396716051320554906013074e-123 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.6124499519984951434514169271136e-115 estimated_step_error = 4.6124499519984951434514169271136e-115 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 = 3.0953921145061884358451603243403e-107 estimated_step_error = 3.0953921145061884358451603243403e-107 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 = 2.0773218772353800142339251534024e-99 estimated_step_error = 2.0773218772353800142339251534024e-99 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 = 1.3941199885175437103096968951314e-91 estimated_step_error = 1.3941199885175437103096968951314e-91 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 = 9.3564906260931470770328224636127e-84 estimated_step_error = 9.3564906260931470770328224636127e-84 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 = 6.2799873957036472828680343021075e-76 estimated_step_error = 6.2799873957036472828680343021075e-76 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.2157076233574059713240087837619e-68 estimated_step_error = 4.2157076233574059713240087837619e-68 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 = 2.8308322136530815525163584828263e-60 estimated_step_error = 2.8308322136530815525163584828263e-60 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 = 1.9020502070240742375686819415174e-52 estimated_step_error = 1.9020502070240742375686819415174e-52 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = 1.0067379469990854670966360484231 y[1] (numeric) = 1.0067379469990854670966360484231 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.99 y[1] (analytic) = 1.0068056644922305447989653325038 y[1] (numeric) = 1.0068056644922305447989653325038 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.98 y[1] (analytic) = 1.0068740625574962515372906482734 y[1] (numeric) = 1.0068740625574962515372906482734 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.97 y[1] (analytic) = 1.0069431480347461124600022155601 y[1] (numeric) = 1.00694314803474611246000221556 absolute error = 1e-31 relative error = 9.9310472686735385727626713945250e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.96 y[1] (analytic) = 1.0070129278325854239761383024475 y[1] (numeric) = 1.0070129278325854239761383024474 absolute error = 1e-31 relative error = 9.9303591082223791072002433493796e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.95 y[1] (analytic) = 1.0070834089290521200422164000473 y[1] (numeric) = 1.0070834089290521200422164000473 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.94 y[1] (analytic) = 1.0071545983723145817706798693521 y[1] (numeric) = 1.007154598372314581770679869352 absolute error = 1e-31 relative error = 9.9289622627561122127996230791568e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=4000168, alloc=3079628, time=0.15 x[1] = -4.93 y[1] (analytic) = 1.0072265032813764601415024147785 y[1] (numeric) = 1.0072265032813764601415024147784 absolute error = 1e-31 relative error = 9.9282534439092526446011658340670e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.92 y[1] (analytic) = 1.0072991308467885822998088990669 y[1] (numeric) = 1.0072991308467885822998088990668 absolute error = 1e-31 relative error = 9.9275376040416857170774081411481e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.91 y[1] (analytic) = 1.0073724883313680126307355188432 y[1] (numeric) = 1.007372488331368012630735518843 absolute error = 2e-31 relative error = 1.9853629349287075526147880025351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = 1.0074465830709243405182360464201 y[1] (numeric) = 1.00744658307092434051823604642 absolute error = 1e-31 relative error = 9.9260845865571802696463205777188e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.89 y[1] (analytic) = 1.0075214224749932674172152602805 y[1] (numeric) = 1.0075214224749932674172152602804 absolute error = 1e-31 relative error = 9.9253472699715231166426641926472e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.88 y[1] (analytic) = 1.0075970140275775665983081021806 y[1] (numeric) = 1.0075970140275775665983081021805 absolute error = 1e-31 relative error = 9.9246026544162660741430998839844e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.87 y[1] (analytic) = 1.0076733652878954896618965073037 y[1] (numeric) = 1.0076733652878954896618965073036 absolute error = 1e-31 relative error = 9.9238506687561084363750361143262e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.86 y[1] (analytic) = 1.00775048389113669466263898332 y[1] (numeric) = 1.0077504838911366946626389833199 absolute error = 1e-31 relative error = 9.9230912411849166739567711237250e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.85 y[1] (analytic) = 1.0078283775492257714379553335143 y[1] (numeric) = 1.0078283775492257714379553335142 absolute error = 1e-31 relative error = 9.9223242992198499906928184684916e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.84 y[1] (analytic) = 1.0079070540515934404936356456817 y[1] (numeric) = 1.0079070540515934404936356456816 absolute error = 1e-31 relative error = 9.9215497696954436756552094551766e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.83 y[1] (analytic) = 1.0079865212659555025671047755709 y[1] (numeric) = 1.0079865212659555025671047755708 absolute error = 1e-31 relative error = 9.9207675787576501459388760495678e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.82 y[1] (analytic) = 1.0080667871390996167639477781226 y[1] (numeric) = 1.0080667871390996167639477781225 absolute error = 1e-31 relative error = 9.9199776518578375802789425893765e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.81 y[1] (analytic) = 1.0081478596976799859461655896795 y[1] (numeric) = 1.0081478596976799859461655896794 absolute error = 1e-31 relative error = 9.9191799137467460486663417203571e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8 y[1] (analytic) = 1.0082297470490200288413620267661 y[1] (numeric) = 1.008229747049020028841362026766 absolute error = 1e-31 relative error = 9.9183742884684010481986457496691e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -4.79 y[1] (analytic) = 1.0083124573819231191407419157932 y[1] (numeric) = 1.0083124573819231191407419157931 absolute error = 1e-31 relative error = 9.9175606993539843606584427182949e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.78 y[1] (analytic) = 1.0083959989674914726605057716668 y[1] (numeric) = 1.0083959989674914726605057716666 absolute error = 2e-31 relative error = 1.9833478138031324305450216674911e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.77 y[1] (analytic) = 1.0084803801599532644560395730107 y[1] (numeric) = 1.0084803801599532644560395730106 absolute error = 1e-31 relative error = 9.9159093193403702453006000972383e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -4.76 y[1] (analytic) = 1.0085656093974980586013003195423 y[1] (numeric) = 1.0085656093974980586013003195422 absolute error = 1e-31 relative error = 9.9150713714835564841691465355643e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.75 y[1] (analytic) = 1.0086516952031206341770715039573 y[1] (numeric) = 1.0086516952031206341770715039571 absolute error = 2e-31 relative error = 1.9828450291725760300235380162015e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.74 y[1] (analytic) = 1.008738646185473291851390514541 y[1] (numeric) = 1.0087386461854732918513905145409 absolute error = 1e-31 relative error = 9.9133705621518683527219827276012e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.73 y[1] (analytic) = 1.0088264710397267262835162690968 y[1] (numeric) = 1.0088264710397267262835162690966 absolute error = 2e-31 relative error = 1.9825015078547058716511393177356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.72 y[1] (analytic) = 1.0089151785484395504393948730148 y[1] (numeric) = 1.0089151785484395504393948730146 absolute error = 2e-31 relative error = 1.9823271990787845617220425764169e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=8001600, alloc=4193536, time=0.30 TOP MAIN SOLVE Loop x[1] = -4.71 y[1] (analytic) = 1.009004777582436558771779454061 y[1] (numeric) = 1.0090047775824365587717794540609 absolute error = 1e-31 relative error = 9.9107558479156867947243605284125e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.7 y[1] (analytic) = 1.0090952771016958170920540742914 y[1] (numeric) = 1.0090952771016958170920540742913 absolute error = 1e-31 relative error = 9.9098670134715217548198077183492e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.69 y[1] (analytic) = 1.0091866861562446678434881455062 y[1] (numeric) = 1.0091866861562446678434881455061 absolute error = 1e-31 relative error = 9.9089694079176311747226363268872e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.68 y[1] (analytic) = 1.0092790138870647403771953472374 y[1] (numeric) = 1.0092790138870647403771953472373 absolute error = 1e-31 relative error = 9.9080629463271190747284714613768e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.67 y[1] (analytic) = 1.0093722695270060567325788209032 y[1] (numeric) = 1.0093722695270060567325788209031 absolute error = 1e-31 relative error = 9.9071475429833442748410703508965e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.66 y[1] (analytic) = 1.0094664624017103243336024420067 y[1] (numeric) = 1.0094664624017103243336024420066 absolute error = 1e-31 relative error = 9.9062231113732314377862222560719e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.65 y[1] (analytic) = 1.0095616019305435079309272106497 y[1] (numeric) = 1.0095616019305435079309272106497 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.64 y[1] (analytic) = 1.0096576976275377740478841198775 y[1] (numeric) = 1.0096576976275377740478841198775 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.63 y[1] (analytic) = 1.0097547591023429021255130554615 y[1] (numeric) = 1.0097547591023429021255130554615 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.62 y[1] (analytic) = 1.0098527960611872575085750762749 y[1] (numeric) = 1.0098527960611872575085750762749 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.61 y[1] (analytic) = 1.0099518183078484223706374899795 y[1] (numeric) = 1.0099518183078484223706374899794 absolute error = 1e-31 relative error = 9.9014624447676873306209070173920e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6 y[1] (analytic) = 1.0100518357446335816421330943316 y[1] (numeric) = 1.0100518357446335816421330943315 absolute error = 1e-31 relative error = 9.9004819813309567842705096155051e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -4.59 y[1] (analytic) = 1.0101528583733697619808033810288 y[1] (numeric) = 1.0101528583733697619808033810287 absolute error = 1e-31 relative error = 9.8994918611652624558191624573620e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.58 y[1] (analytic) = 1.0102548962964040228092479483096 y[1] (numeric) = 1.0102548962964040228092479483095 absolute error = 1e-31 relative error = 9.8984919911400727862257840773689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.57 y[1] (analytic) = 1.0103579597176136994395173725574 y[1] (numeric) = 1.0103579597176136994395173725573 absolute error = 1e-31 relative error = 9.8974822772662803637833128948875e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.56 y[1] (analytic) = 1.0104620589434267993099038702723 y[1] (numeric) = 1.0104620589434267993099038702722 absolute error = 1e-31 relative error = 9.8964626246890825281234740145476e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.55 y[1] (analytic) = 1.0105672043838526533744037625093 y[1] (numeric) = 1.0105672043838526533744037625092 absolute error = 1e-31 relative error = 9.8954329376808193060881743383969e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.54 y[1] (analytic) = 1.0106734065535229257108495670498 y[1] (numeric) = 1.0106734065535229257108495670496 absolute error = 2e-31 relative error = 1.9788786239267537573432532382456e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.53 y[1] (analytic) = 1.0107806760727430854495400424133 y[1] (numeric) = 1.0107806760727430854495400424132 absolute error = 1e-31 relative error = 9.8933430730529000531222045416999e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.52 y[1] (analytic) = 1.0108890236685544461704372762439 y[1] (numeric) = 1.0108890236685544461704372762438 absolute error = 1e-31 relative error = 9.8922826995485837998281423503751e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.51 y[1] (analytic) = 1.0109984601758068789737555735586 y[1] (numeric) = 1.0109984601758068789737555735584 absolute error = 2e-31 relative error = 1.9782423799658521550315608222319e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.5 y[1] (analytic) = 1.0111089965382423064961431342869 y[1] (numeric) = 1.0111089965382423064961431342867 absolute error = 2e-31 relative error = 1.9780261147388136399227292430062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=12003516, alloc=4259060, time=0.45 TOP MAIN SOLVE Loop x[1] = -4.49 y[1] (analytic) = 1.0112206438095890862227610529593 y[1] (numeric) = 1.0112206438095890862227610529591 absolute error = 2e-31 relative error = 1.9778077240050848645486013421971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.48 y[1] (analytic) = 1.0113334131546673925345028375762 y[1] (numeric) = 1.011333413154667392534502837576 absolute error = 2e-31 relative error = 1.9775871873563142585717748215029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.47 y[1] (analytic) = 1.0114473158505057080294803243879 y[1] (numeric) = 1.0114473158505057080294803243878 absolute error = 1e-31 relative error = 9.8868224209890765261213281057043e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.46 y[1] (analytic) = 1.0115623632874685357688385497119 y[1] (numeric) = 1.0115623632874685357688385497118 absolute error = 1e-31 relative error = 9.8856979687352927739114428620900e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.45 y[1] (analytic) = 1.0116785669703954452190639236115 y[1] (numeric) = 1.0116785669703954452190639236114 absolute error = 1e-31 relative error = 9.8845624751607771001453689198422e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.44 y[1] (analytic) = 1.0117959385197515657963291443707 y[1] (numeric) = 1.0117959385197515657963291443706 absolute error = 1e-31 relative error = 9.8834158344516689931873516268457e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.43 y[1] (analytic) = 1.0119144896727896430631880360715 y[1] (numeric) = 1.0119144896727896430631880360714 absolute error = 1e-31 relative error = 9.8822579398320278503315847189528e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.42 y[1] (analytic) = 1.01203423228472377378420836215 y[1] (numeric) = 1.0120342322847237737842083621499 absolute error = 1e-31 relative error = 9.8810886835561300864390753253886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.41 y[1] (analytic) = 1.0121551783299149372150262940186 y[1] (numeric) = 1.0121551783299149372150262940186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4 y[1] (analytic) = 1.0122773399030684411789393862365 y[1] (numeric) = 1.0122773399030684411789393862365 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.39 y[1] (analytic) = 1.0124007292204434026766435925812 y[1] (numeric) = 1.0124007292204434026766435925812 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.38 y[1] (analytic) = 1.0125253586210743839781832005917 y[1] (numeric) = 1.0125253586210743839781832005916 absolute error = 1e-31 relative error = 9.8762958525983757508630990224003e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.37 y[1] (analytic) = 1.0126512405680053063617409130458 y[1] (numeric) = 1.0126512405680053063617409130457 absolute error = 1e-31 relative error = 9.8750681373687044488197366255369e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.36 y[1] (analytic) = 1.0127783876495357648916702202577 y[1] (numeric) = 1.0127783876495357648916702202576 absolute error = 1e-31 relative error = 9.8738283932066130497011202952860e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.35 y[1] (analytic) = 1.0129068125804798688682864655417 y[1] (numeric) = 1.0129068125804798688682864655416 absolute error = 1e-31 relative error = 9.8725765053588839767593044649357e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.34 y[1] (analytic) = 1.0130365282034377338345106201543 y[1] (numeric) = 1.0130365282034377338345106201542 absolute error = 1e-31 relative error = 9.8713123580394749436990192078239e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.33 y[1] (analytic) = 1.0131675474900797522896260122973 y[1] (numeric) = 1.0131675474900797522896260122972 absolute error = 1e-31 relative error = 9.8700358344214664064609992488146e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.32 y[1] (analytic) = 1.013299883542443771538289615015 y[1] (numeric) = 1.0132998835424437715382896150148 absolute error = 2e-31 relative error = 1.9737493633257943949513494633564e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.31 y[1] (analytic) = 1.0134335495942453083936637792599 y[1] (numeric) = 1.0134335495942453083936637792597 absolute error = 2e-31 relative error = 1.9734890371458024412706491471097e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.3 y[1] (analytic) = 1.0135685590122009317572305745258 y[1] (numeric) = 1.0135685590122009317572305745256 absolute error = 2e-31 relative error = 1.9732261643446704449592628233718e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.29 y[1] (analytic) = 1.0137049252973649454146495409732 y[1] (numeric) = 1.013704925297364945414649540973 absolute error = 2e-31 relative error = 1.9729607207080607238653791729298e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.28 y[1] (analytic) = 1.0138426620864795047170523448676 y[1] (numeric) = 1.0138426620864795047170523448674 absolute error = 2e-31 relative error = 1.9726926818052982208382587002422e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16007952, alloc=4259060, time=0.60 TOP MAIN SOLVE Loop x[1] = -4.27 y[1] (analytic) = 1.0139817831533383021605675677785 y[1] (numeric) = 1.0139817831533383021605675677783 absolute error = 2e-31 relative error = 1.9724220229877168866760119287828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.455e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.26 y[1] (analytic) = 1.0141223024101639582337699904576 y[1] (numeric) = 1.0141223024101639582337699904574 absolute error = 2e-31 relative error = 1.9721487193869992172113456587938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.25 y[1] (analytic) = 1.014264233908999255273286945856 y[1] (numeric) = 1.0142642339089992552732869458558 absolute error = 2e-31 relative error = 1.9718727459135090515125449537487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.24 y[1] (analytic) = 1.0144075918431123534521066673262 y[1] (numeric) = 1.014407591843112353452106667326 absolute error = 2e-31 relative error = 1.9715940772546177421829098158680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.23 y[1] (analytic) = 1.0145523905484161294233584800719 y[1] (numeric) = 1.0145523905484161294233584800717 absolute error = 2e-31 relative error = 1.9713126878730238128299309351177e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.22 y[1] (analytic) = 1.0146986445049017795546120000092 y[1] (numeric) = 1.014698644504901779554612000009 absolute error = 2e-31 relative error = 1.9710285520050662219468699321761e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.21 y[1] (analytic) = 1.0148463683380868311142134433043 y[1] (numeric) = 1.0148463683380868311142134433041 absolute error = 2e-31 relative error = 1.9707416436590313567053152769389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -4.2 y[1] (analytic) = 1.0149955768204777062119843602287 y[1] (numeric) = 1.0149955768204777062119843602285 absolute error = 2e-31 relative error = 1.9704519366134538844989319982663e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.19 y[1] (analytic) = 1.0151462848730469847518956705525 y[1] (numeric) = 1.0151462848730469847518956705523 absolute error = 2e-31 relative error = 1.9701594044154115945072348782972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.18 y[1] (analytic) = 1.015298507566725514124243324443 y[1] (numeric) = 1.0152985075667255141242433244428 absolute error = 2e-31 relative error = 1.9698640203788143660650212096576e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.17 y[1] (analytic) = 1.0154522601239095148495382353233 y[1] (numeric) = 1.0154522601239095148495382353231 absolute error = 2e-31 relative error = 1.9695657575826874052293368973881e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.16 y[1] (analytic) = 1.0156075579199828328859307992401 y[1] (numeric) = 1.0156075579199828328859307992399 absolute error = 2e-31 relative error = 1.9692645888694488956327612040250e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.15 y[1] (analytic) = 1.0157644164848544908266692910111 y[1] (numeric) = 1.0157644164848544908266692910109 absolute error = 2e-31 relative error = 1.9689604868431822145006288620803e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.14 y[1] (analytic) = 1.0159228515045116917439931799265 y[1] (numeric) = 1.0159228515045116917439931799263 absolute error = 2e-31 relative error = 1.9686534238679028695918169101620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.13 y[1] (analytic) = 1.0160828788225884309811399285206 y[1] (numeric) = 1.0160828788225884309811399285204 absolute error = 2e-31 relative error = 1.9683433720658203177991655251048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.12 y[1] (analytic) = 1.0162445144419498727549516559441 y[1] (numeric) = 1.0162445144419498727549516559439 absolute error = 2e-31 relative error = 1.9680303033155948312177397420157e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.165e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.11 y[1] (analytic) = 1.0164077745262926500080622448391 y[1] (numeric) = 1.0164077745262926500080622448388 absolute error = 3e-31 relative error = 2.9515712838758843724873578664299e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.1 y[1] (analytic) = 1.0165726754017612475419836980835 y[1] (numeric) = 1.0165726754017612475419836980832 absolute error = 3e-31 relative error = 2.9510925018856771797752841008200e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.09 y[1] (analytic) = 1.0167392335585806300707520444753 y[1] (numeric) = 1.016739233558580630070752044475 absolute error = 3e-31 relative error = 2.9506090657090311464196015358218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.08 y[1] (analytic) = 1.0169074656527052784592986858592 y[1] (numeric) = 1.016907465652705278459298685859 absolute error = 2e-31 relative error = 1.9667472877842367534077639022472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.07 y[1] (analytic) = 1.0170773885074847990515452242772 y[1] (numeric) = 1.017077388507484799051545224277 absolute error = 2e-31 relative error = 1.9664187038263723539171567955079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.06 y[1] (analytic) = 1.0172490191153462726505425910253 y[1] (numeric) = 1.0172490191153462726505425910251 absolute error = 2e-31 relative error = 1.9660869289795984566442243666688e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed bytes used=20008956, alloc=4259060, time=0.75 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.05 y[1] (analytic) = 1.0174223746394935113869544536867 y[1] (numeric) = 1.0174223746394935113869544536865 absolute error = 2e-31 relative error = 1.9657519333685445309604081259138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -4.04 y[1] (analytic) = 1.017597472415623393402987801592 y[1] (numeric) = 1.0175974724156233934029878015917 absolute error = 3e-31 relative error = 2.9481205302902837213806840053325e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.03 y[1] (analytic) = 1.017774329953659446986669386436 y[1] (numeric) = 1.0177743299536594469866693864357 absolute error = 3e-31 relative error = 2.9476082385931209287259726743155e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.02 y[1] (analytic) = 1.0179529649395028575163261039565 y[1] (numeric) = 1.0179529649395028575163261039562 absolute error = 3e-31 relative error = 2.9470909789808319708246572893625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.01 y[1] (analytic) = 1.01813339523680107231742294203 y[1] (numeric) = 1.0181333952368010723174229420297 absolute error = 3e-31 relative error = 2.9465687050784238061265723352286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4 y[1] (analytic) = 1.0183156388887341802937180212732 y[1] (numeric) = 1.018315638888734180293718021273 absolute error = 2e-31 relative error = 1.9640275800758168839464137241010e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.99 y[1] (analytic) = 1.0184997141198192449721864983093 y[1] (numeric) = 1.0184997141198192449721864983091 absolute error = 2e-31 relative error = 1.9636726179431349644399573462294e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.98 y[1] (analytic) = 1.0186856393377327713965214399713 y[1] (numeric) = 1.0186856393377327713965214399711 absolute error = 2e-31 relative error = 1.9633142186045134261763179194024e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.97 y[1] (analytic) = 1.0188734331351514891174197460049 y[1] (numeric) = 1.0188734331351514891174197460046 absolute error = 3e-31 relative error = 2.9444285251101017767253548619969e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.96 y[1] (analytic) = 1.0190631142916116353594861398 y[1] (numeric) = 1.0190631142916116353594861397998 absolute error = 2e-31 relative error = 1.9625869800912907943799282923468e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.95 y[1] (analytic) = 1.0192547017753869242946213253559 y[1] (numeric) = 1.0192547017753869242946213253557 absolute error = 2e-31 relative error = 1.9622180761259218966873445832043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.94 y[1] (analytic) = 1.0194482147453853902203866289042 y[1] (numeric) = 1.019448214745385390220386628904 absolute error = 2e-31 relative error = 1.9618456053694836802073369207277e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.93 y[1] (analytic) = 1.0196436725530652943292436695736 y[1] (numeric) = 1.0196436725530652943292436695735 absolute error = 1e-31 relative error = 9.8073476736840832100654563954738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.92 y[1] (analytic) = 1.0198410947443702866609425773594 y[1] (numeric) = 1.0198410947443702866609425773592 absolute error = 2e-31 relative error = 1.9610898308636139351648760888659e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.91 y[1] (analytic) = 1.0200405010616840167558666375535 y[1] (numeric) = 1.0200405010616840167558666375534 absolute error = 1e-31 relative error = 9.8035323005231130026550313349086e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.9 y[1] (analytic) = 1.0202419114458043884720275437437 y[1] (numeric) = 1.0202419114458043884720275437435 absolute error = 2e-31 relative error = 1.9603193885318449868951736106286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.89 y[1] (analytic) = 1.0204453460379376563928381767342 y[1] (numeric) = 1.0204453460379376563928381767341 absolute error = 1e-31 relative error = 9.7996429096637033557705749908180e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.88 y[1] (analytic) = 1.0206508251817125632369654392163 y[1] (numeric) = 1.0206508251817125632369654392162 absolute error = 1e-31 relative error = 9.7976700290421459907924515078549e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.87 y[1] (analytic) = 1.0208583694252147196856825849039 y[1] (numeric) = 1.0208583694252147196856825849038 absolute error = 1e-31 relative error = 9.7956781268594698381282294031717e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.86 y[1] (analytic) = 1.0210679995230414300673990995446 y[1] (numeric) = 1.0210679995230414300673990995445 absolute error = 1e-31 relative error = 9.7936670277309380177839421104296e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.85 y[1] (analytic) = 1.0212797364383771693836489472373 y[1] (numeric) = 1.0212797364383771693836489472373 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.84 y[1] (analytic) = 1.0214936013450899192259693508355 y[1] (numeric) = 1.0214936013450899192259693508355 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 bytes used=24010964, alloc=4324584, time=0.90 TOP MAIN SOLVE Loop x[1] = -3.83 y[1] (analytic) = 1.0217096156298485722190087467336 y[1] (numeric) = 1.0217096156298485722190087467336 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.82 y[1] (analytic) = 1.0219278008942616167320727344178 y[1] (numeric) = 1.0219278008942616167320727344178 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.81 y[1] (analytic) = 1.0221481789570373157293614185755 y[1] (numeric) = 1.0221481789570373157293614185756 absolute error = 1e-31 relative error = 9.7833173368303946994183403370637e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8 y[1] (analytic) = 1.0223707718561655957785833225408 y[1] (numeric) = 1.0223707718561655957785833225409 absolute error = 1e-31 relative error = 9.7811872906386952604774870301435e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.79 y[1] (analytic) = 1.0225956018511218644086649813674 y[1] (numeric) = 1.0225956018511218644086649813674 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.78 y[1] (analytic) = 1.0228226914250929762001285060763 y[1] (numeric) = 1.0228226914250929762001285060763 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.77 y[1] (analytic) = 1.0230520632872255702066011347591 y[1] (numeric) = 1.0230520632872255702066011347592 absolute error = 1e-31 relative error = 9.7746736054355268917485844818480e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.76 y[1] (analytic) = 1.0232837403748970035430725422555 y[1] (numeric) = 1.0232837403748970035430725422556 absolute error = 1e-31 relative error = 9.7724605653719600946646641496976e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.75 y[1] (analytic) = 1.0235177458560091082361511851004 y[1] (numeric) = 1.0235177458560091082361511851005 absolute error = 1e-31 relative error = 9.7702263008997438504609611330987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.74 y[1] (analytic) = 1.0237541031313050007139161777898 y[1] (numeric) = 1.0237541031313050007139161777899 absolute error = 1e-31 relative error = 9.7679706185435591958341833488479e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.73 y[1] (analytic) = 1.0239928358367091756182443665626 y[1] (numeric) = 1.0239928358367091756182443665627 absolute error = 1e-31 relative error = 9.7656933232632968473375828888476e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.72 y[1] (analytic) = 1.024233967845691117950943918083 y[1] (numeric) = 1.0242339678456911179509439180831 absolute error = 1e-31 relative error = 9.7633942184453879065769525937927e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.71 y[1] (analytic) = 1.0244775232716526699168787197371 y[1] (numeric) = 1.0244775232716526699168787197372 absolute error = 1e-31 relative error = 9.7610731058941723893048341933284e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7 y[1] (analytic) = 1.0247235264703393912027573829834 y[1] (numeric) = 1.0247235264703393912027573829835 absolute error = 1e-31 relative error = 9.7587297858233079871961975186281e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.69 y[1] (analytic) = 1.024972002042276153829624202256 y[1] (numeric) = 1.0249720020422761538296242022561 absolute error = 1e-31 relative error = 9.7563640568472215227542482840406e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.68 y[1] (analytic) = 1.0252229748352272151405669876582 y[1] (numeric) = 1.0252229748352272151405669876583 absolute error = 1e-31 relative error = 9.7539757159726056101816175413068e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.67 y[1] (analytic) = 1.0254764699466810149329906098868 y[1] (numeric) = 1.0254764699466810149329906098868 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.66 y[1] (analytic) = 1.0257325127263599452172401559202 y[1] (numeric) = 1.0257325127263599452172401559202 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.65 y[1] (analytic) = 1.0259911287787553435806410395574 y[1] (numeric) = 1.0259911287787553435806410395574 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.64 y[1] (analytic) = 1.0262523439656879636584049723293 y[1] (numeric) = 1.0262523439656879636584049723293 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -3.63 y[1] (analytic) = 1.0265161844088941787605826178852 y[1] (numeric) = 1.0265161844088941787605826178852 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.62 y[1] (analytic) = 1.0267826764926381772775808019925 y[1] (numeric) = 1.0267826764926381772775808019925 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 bytes used=28013408, alloc=4324584, time=1.05 TOP MAIN SOLVE Loop x[1] = -3.61 y[1] (analytic) = 1.0270518468663504110859616666317 y[1] (numeric) = 1.0270518468663504110859616666317 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -3.6 y[1] (analytic) = 1.0273237224472925608015630624356 y[1] (numeric) = 1.0273237224472925608015630624356 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.59 y[1] (analytic) = 1.0275983304232492843786863032922 y[1] (numeric) = 1.0275983304232492843786863032923 absolute error = 1e-31 relative error = 9.7314288121519034769885014814130e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.58 y[1] (analytic) = 1.0278756982552470182324543331974 y[1] (numeric) = 1.0278756982552470182324543331975 absolute error = 1e-31 relative error = 9.7288028279823696028136184499231e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = -3.57 y[1] (analytic) = 1.0281558536803001027667182163266 y[1] (numeric) = 1.0281558536803001027667182163267 absolute error = 1e-31 relative error = 9.7261518904987431602638499671080e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.56 y[1] (analytic) = 1.0284388247141845069223531865445 y[1] (numeric) = 1.0284388247141845069223531865446 absolute error = 1e-31 relative error = 9.7234757767717686305421014316514e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.55 y[1] (analytic) = 1.0287246396542394291207105307843 y[1] (numeric) = 1.0287246396542394291207105307845 absolute error = 2e-31 relative error = 1.9441548524318539620617803033737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.54 y[1] (analytic) = 1.0290133270821970547646543267218 y[1] (numeric) = 1.0290133270821970547646543267219 absolute error = 1e-31 relative error = 9.7180471202985742755568090094584e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.53 y[1] (analytic) = 1.029304915867040753275291277527 y[1] (numeric) = 1.0293049158670407532752912775272 absolute error = 2e-31 relative error = 1.9430588246198055053914143116204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.52 y[1] (analytic) = 1.0295994351678920004864791554834 y[1] (numeric) = 1.0295994351678920004864791554835 absolute error = 1e-31 relative error = 9.7125150407346002671961940007315e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.51 y[1] (analytic) = 1.0298969144369263150917590819967 y[1] (numeric) = 1.0298969144369263150917590819968 absolute error = 1e-31 relative error = 9.7097096416365923256556132401645e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.5 y[1] (analytic) = 1.0301973834223185007397862923636 y[1] (numeric) = 1.0301973834223185007397862923638 absolute error = 2e-31 relative error = 1.9413755384972873622694208837717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -3.49 y[1] (analytic) = 1.030500872171217488304923304969 y[1] (numeric) = 1.0305008721712174883049233049692 absolute error = 2e-31 relative error = 1.9408037916417216282592652870365e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.48 y[1] (analytic) = 1.0308074110327510758197015977179 y[1] (numeric) = 1.030807411032751075819701597718 absolute error = 1e-31 relative error = 9.7011332019636376585630352733735e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.47 y[1] (analytic) = 1.0311170306610608665456489961601 y[1] (numeric) = 1.0311170306610608665456489961602 absolute error = 1e-31 relative error = 9.6982201851412406217944310682952e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.46 y[1] (analytic) = 1.0314297620183677086788189795365 y[1] (numeric) = 1.0314297620183677086788189795367 absolute error = 2e-31 relative error = 1.9390559334707116833245641511998e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.45 y[1] (analytic) = 1.0317456363780679432365469992797 y[1] (numeric) = 1.0317456363780679432365469992799 absolute error = 2e-31 relative error = 1.9384622812857039816669397228148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.44 y[1] (analytic) = 1.0320646853278607697528027007736 y[1] (numeric) = 1.0320646853278607697528027007738 absolute error = 2e-31 relative error = 1.9378630316806651850098690529583e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.43 y[1] (analytic) = 1.0323869407729070425213137303623 y[1] (numeric) = 1.0323869407729070425213137303625 absolute error = 2e-31 relative error = 1.9372581355036121862288849368170e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.42 y[1] (analytic) = 1.0327124349390198132687177789643 y[1] (numeric) = 1.0327124349390198132687177789645 absolute error = 2e-31 relative error = 1.9366475432418872043693065838785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -3.41 y[1] (analytic) = 1.0330412003758869393146689719212 y[1] (numeric) = 1.0330412003758869393146689719214 absolute error = 2e-31 relative error = 1.9360312050209334883516658689408e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.4 y[1] (analytic) = 1.0333732699603260794824001314709 y[1] (numeric) = 1.0333732699603260794824001314711 absolute error = 2e-31 relative error = 1.9354090706030989805224487577461e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=32014600, alloc=4324584, time=1.20 TOP MAIN SOLVE Loop x[1] = -3.39 y[1] (analytic) = 1.0337086768995724032620444737059 y[1] (numeric) = 1.033708676899572403262044473706 absolute error = 1e-31 relative error = 9.6739054469323440487146388468089e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -3.38 y[1] (analytic) = 1.0340474547345993420003728389543 y[1] (numeric) = 1.0340474547345993420003728389544 absolute error = 1e-31 relative error = 9.6707360520186374923638905833581e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.37 y[1] (analytic) = 1.0343896373434727141948327311903 y[1] (numeric) = 1.0343896373434727141948327311904 absolute error = 1e-31 relative error = 9.6675369116052589159806238498543e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -3.36 y[1] (analytic) = 1.0347352589447385603072136841051 y[1] (numeric) = 1.0347352589447385603072136841053 absolute error = 2e-31 relative error = 1.9328615534370349625534177169317e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = -3.35 y[1] (analytic) = 1.0350843541008450258832435254655 y[1] (numeric) = 1.0350843541008450258832435254657 absolute error = 2e-31 relative error = 1.9322096716816437026806910525550e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.34 y[1] (analytic) = 1.0354369577215986351692790781561 y[1] (numeric) = 1.0354369577215986351692790781562 absolute error = 1e-31 relative error = 9.6577584230760412225789616177189e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.33 y[1] (analytic) = 1.0357931050676553008563332045916 y[1] (numeric) = 1.0357931050676553008563332045917 absolute error = 1e-31 relative error = 9.6544376971372348660319144161987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -3.32 y[1] (analytic) = 1.0361528317540464190553217816872 y[1] (numeric) = 1.0361528317540464190553217816873 absolute error = 1e-31 relative error = 9.6510859146826316262203088385288e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.31 y[1] (analytic) = 1.0365161737537404021159665533578 y[1] (numeric) = 1.036516173753740402115966553358 absolute error = 2e-31 relative error = 1.9295405615881570245498471323758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3 y[1] (analytic) = 1.0368831674012400054456037047415 y[1] (numeric) = 1.0368831674012400054456037047417 absolute error = 2e-31 relative error = 1.9288576214547276544452870519188e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.29 y[1] (analytic) = 1.0372538493962158080635778213451 y[1] (numeric) = 1.0372538493962158080635778213453 absolute error = 2e-31 relative error = 1.9281683082344765882573216316909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.28 y[1] (analytic) = 1.0376282568071762102423045830638 y[1] (numeric) = 1.037628256807176210242304583064 absolute error = 2e-31 relative error = 1.9274725672507033172201622657018e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.27 y[1] (analytic) = 1.0380064270751743152378246409055 y[1] (numeric) = 1.0380064270751743152378246409057 absolute error = 2e-31 relative error = 1.9267703434510202303501935379574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.26 y[1] (analytic) = 1.0383883980175520658011108102137 y[1] (numeric) = 1.0383883980175520658011108102138 absolute error = 1e-31 relative error = 9.6303079070332295853817841165312e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.25 y[1] (analytic) = 1.0387742078317220098868998352676 y[1] (numeric) = 1.0387742078317220098868998352677 absolute error = 1e-31 relative error = 9.6267311265587053980228583396150e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.24 y[1] (analytic) = 1.0391638950989870737397710903658 y[1] (numeric) = 1.0391638950989870737397710903659 absolute error = 1e-31 relative error = 9.6231210949139407913811391888854e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.23 y[1] (analytic) = 1.0395574987883987243379639801109 y[1] (numeric) = 1.0395574987883987243379639801111 absolute error = 2e-31 relative error = 1.9238955058580157895431758444929e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.22 y[1] (analytic) = 1.0399550582606539070143935667244 y[1] (numeric) = 1.0399550582606539070143935667246 absolute error = 2e-31 relative error = 1.9231600289968692326202923391622e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.21 y[1] (analytic) = 1.040356613272031147951873984794 y[1] (numeric) = 1.0403566132720311479518739847942 absolute error = 2e-31 relative error = 1.9224177310795279173867269360006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2 y[1] (analytic) = 1.0407622039783662151660792621444 y[1] (numeric) = 1.0407622039783662151660792621446 absolute error = 2e-31 relative error = 1.9216685544064712826832642230889e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.19 y[1] (analytic) = 1.0411718709390677355456529047735 y[1] (numeric) = 1.0411718709390677355456529047737 absolute error = 2e-31 relative error = 1.9209124408980940907905569549750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.18 y[1] (analytic) = 1.041585655121173169514516615502 y[1] (numeric) = 1.0415856551211731695145166155022 absolute error = 2e-31 relative error = 1.9201493320943724205657793464199e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=36015596, alloc=4324584, time=1.36 TOP MAIN SOLVE Loop x[1] = -3.17 y[1] (analytic) = 1.04200359790344554891722436736 y[1] (numeric) = 1.0420035979034455489172243673602 absolute error = 2e-31 relative error = 1.9193791691545815584577612768612e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.16 y[1] (analytic) = 1.042425741080511387804564326735 y[1] (numeric) = 1.0424257410805113878045643267352 absolute error = 2e-31 relative error = 1.9186018928570670234069109590364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -3.15 y[1] (analytic) = 1.0428521268670401799139354569562 y[1] (numeric) = 1.0428521268670401799139354569564 absolute error = 2e-31 relative error = 1.9178174435990699784599936654569e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.14 y[1] (analytic) = 1.0432827979019659007977297661522 y[1] (numeric) = 1.0432827979019659007977297661524 absolute error = 2e-31 relative error = 1.9170257613966082987846433611735e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.13 y[1] (analytic) = 1.0437177972527509367534509677739 y[1] (numeric) = 1.0437177972527509367534509677741 absolute error = 2e-31 relative error = 1.9162267858844145826476308520059e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.12 y[1] (analytic) = 1.0441571684196928669520158516001 y[1] (numeric) = 1.0441571684196928669520158516003 absolute error = 2e-31 relative error = 1.9154204563159324088174318686373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.11 y[1] (analytic) = 1.0446009553402745294460401924352 y[1] (numeric) = 1.0446009553402745294460401924354 absolute error = 2e-31 relative error = 1.9146067115633721607583090313016e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.1 y[1] (analytic) = 1.0450492023935578060683350921783 y[1] (numeric) = 1.0450492023935578060683350921785 absolute error = 2e-31 relative error = 1.9137854901178277548924575126578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.09 y[1] (analytic) = 1.0455019544046215656027651045195 y[1] (numeric) = 1.0455019544046215656027651045196 absolute error = 1e-31 relative error = 9.5647836504472781355550594734069e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.08 y[1] (analytic) = 1.0459592566490442090254835263785 y[1] (numeric) = 1.0459592566490442090254835263786 absolute error = 1e-31 relative error = 9.5606018460385867430292216225245e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.07 y[1] (analytic) = 1.0464211548574312650748044464352 y[1] (numeric) = 1.0464211548574312650748044464353 absolute error = 1e-31 relative error = 9.5563817241084362948189812930388e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.06 y[1] (analytic) = 1.0468876952199884889130415468398 y[1] (numeric) = 1.04688769521998848891304154684 absolute error = 2e-31 relative error = 1.9104245939004265213046888670207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.05 y[1] (analytic) = 1.0473589243911409211939907702397 y[1] (numeric) = 1.0473589243911409211939907702399 absolute error = 2e-31 relative error = 1.9095650530334250210452728218919e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.04 y[1] (analytic) = 1.0478348894941983694458128291081 y[1] (numeric) = 1.0478348894941983694458128291083 absolute error = 2e-31 relative error = 1.9086976584311125466240351323001e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.03 y[1] (analytic) = 1.0483156381260677783213417597388 y[1] (numeric) = 1.0483156381260677783213417597389 absolute error = 1e-31 relative error = 9.5391117296272035360850419101623e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.02 y[1] (analytic) = 1.04880121836201295995677154006 y[1] (numeric) = 1.0488012183620129599567715400601 absolute error = 1e-31 relative error = 9.5346952548526852955132582846479e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -3.01 y[1] (analytic) = 1.0492916787604621604157230951175 y[1] (numeric) = 1.0492916787604621604157230951176 absolute error = 1e-31 relative error = 9.5302385432171646444220454029302e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3 y[1] (analytic) = 1.0497870683678639429793424156501 y[1] (numeric) = 1.0497870683678639429793424156502 absolute error = 1e-31 relative error = 9.5257412682243321912115184822821e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.99 y[1] (analytic) = 1.050287436723591873874805382468 y[1] (numeric) = 1.0502874367235918738748053824681 absolute error = 1e-31 relative error = 9.5212031015008112562458751066214e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.98 y[1] (analytic) = 1.050792833864898500914889398847 y[1] (numeric) = 1.0507928338648985009148893988472 absolute error = 2e-31 relative error = 1.9033247425601895815418777620053e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.97 y[1] (analytic) = 1.0513033103319191204506041173959 y[1] (numeric) = 1.0513033103319191204506041173961 absolute error = 2e-31 relative error = 1.9024005540024000127715581788696e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.96 y[1] (analytic) = 1.0518189171727258330177463441629 y[1] (numeric) = 1.051818917172725833017746344163 absolute error = 1e-31 relative error = 9.5073399391597335087915567342871e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=40016572, alloc=4324584, time=1.51 TOP MAIN SOLVE Loop x[1] = -2.95 y[1] (analytic) = 1.0523397059484323930871555025493 y[1] (numeric) = 1.0523397059484323930871555025494 absolute error = 1e-31 relative error = 9.5026348844144327481602855857569e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.94 y[1] (analytic) = 1.0528657287383503634078987382166 y[1] (numeric) = 1.0528657287383503634078987382167 absolute error = 1e-31 relative error = 9.4978872680973347097048621620406e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.93 y[1] (analytic) = 1.053397038145197089563116793104 y[1] (numeric) = 1.0533970381451970895631167931041 absolute error = 1e-31 relative error = 9.4930967506874933711927667437801e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.92 y[1] (analytic) = 1.053933687300356015540326226409 y[1] (numeric) = 1.0539336873003560155403262264091 absolute error = 1e-31 relative error = 9.4882629908290834750363545446905e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.91 y[1] (analytic) = 1.0544757298691898663521186236729 y[1] (numeric) = 1.0544757298691898663521186236729 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.9 y[1] (analytic) = 1.0550232200564072290299465308342 y[1] (numeric) = 1.0550232200564072290299465308342 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.89 y[1] (analytic) = 1.0555762126114830686535676575805 y[1] (numeric) = 1.0555762126114830686535676575805 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.88 y[1] (analytic) = 1.0561347628341337214722674061654 y[1] (numeric) = 1.0561347628341337214722674061654 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.87 y[1] (analytic) = 1.0566989265798469126217343574206 y[1] (numeric) = 1.0566989265798469126217343574206 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.86 y[1] (analytic) = 1.0572687602654673514429687649702 y[1] (numeric) = 1.0572687602654673514429687649702 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.85 y[1] (analytic) = 1.0578443208748384629674106267774 y[1] (numeric) = 1.0578443208748384629674106267774 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.84 y[1] (analytic) = 1.0584256659645008197461373054073 y[1] (numeric) = 1.0584256659645008197461373054073 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.83 y[1] (analytic) = 1.059012853669447843871062325787 y[1] (numeric) = 1.059012853669447843871062325787 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -2.82 y[1] (analytic) = 1.0596059427089393547631339046828 y[1] (numeric) = 1.0596059427089393547631339046829 absolute error = 1e-31 relative error = 9.4374706642683263064200597200057e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.81 y[1] (analytic) = 1.0602049923923735440871566710524 y[1] (numeric) = 1.0602049923923735440871566710525 absolute error = 1e-31 relative error = 9.4321381919121151518966036670019e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.8 y[1] (analytic) = 1.0608100626252179649956213881839 y[1] (numeric) = 1.060810062625217964995621388184 absolute error = 1e-31 relative error = 9.4267582410113125379170882601282e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.79 y[1] (analytic) = 1.0614212139150001288054095681066 y[1] (numeric) = 1.0614212139150001288054095681067 absolute error = 1e-31 relative error = 9.4213304472363898640683906716129e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.78 y[1] (analytic) = 1.0620385073773583081720328292716 y[1] (numeric) = 1.0620385073773583081720328292716 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.77 y[1] (analytic) = 1.0626620047421531518467667742247 y[1] (numeric) = 1.0626620047421531518467667742247 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.76 y[1] (analytic) = 1.0632917683596407221832481299345 y[1] (numeric) = 1.0632917683596407221832481299346 absolute error = 1e-31 relative error = 9.4047563402349849075859753729787e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.75 y[1] (analytic) = 1.063927861206707572702430025558 y[1] (numeric) = 1.063927861206707572702430025558 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.74 y[1] (analytic) = 1.0645703468931684892288478184621 y[1] (numeric) = 1.0645703468931684892288478184622 absolute error = 1e-31 relative error = 9.3934609668434787113770102795863e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44017732, alloc=4324584, time=1.66 x[1] = -2.73 y[1] (analytic) = 1.065219289668127524377557230193 y[1] (numeric) = 1.0652192896681275243775572301931 absolute error = 1e-31 relative error = 9.3877383718009199532477217780467e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.72 y[1] (analytic) = 1.0658747544264029615004943659454 y[1] (numeric) = 1.0658747544264029615004943659455 absolute error = 1e-31 relative error = 9.3819653373641141663187915148742e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.71 y[1] (analytic) = 1.0665368067150168505940064080062 y[1] (numeric) = 1.0665368067150168505940064080063 absolute error = 1e-31 relative error = 9.3761414862000560380224040169638e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.7 y[1] (analytic) = 1.067205512739749765126551700856 y[1] (numeric) = 1.0672055127397497651265517008561 absolute error = 1e-31 relative error = 9.3702664394300351048584367149103e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.69 y[1] (analytic) = 1.0678809393717614352677143135015 y[1] (numeric) = 1.0678809393717614352677143135017 absolute error = 2e-31 relative error = 1.8728679633298894549194302612849e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.68 y[1] (analytic) = 1.068563154154277919587373193244 y[1] (numeric) = 1.0685631541542779195873731932442 absolute error = 2e-31 relative error = 1.8716722471896521144263194095820e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.67 y[1] (analytic) = 1.0692522253093459839477684894559 y[1] (numeric) = 1.0692522253093459839477684894561 absolute error = 2e-31 relative error = 1.8704660627864289320196865880350e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.66 y[1] (analytic) = 1.0699482217446553630319829218383 y[1] (numeric) = 1.0699482217446553630319829218385 absolute error = 2e-31 relative error = 1.8692493331488547418471268095666e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.65 y[1] (analytic) = 1.0706512130604295867406762781867 y[1] (numeric) = 1.0706512130604295867406762781869 absolute error = 2e-31 relative error = 1.8680219810175624427790278647755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.64 y[1] (analytic) = 1.0713612695563860605454550895863 y[1] (numeric) = 1.0713612695563860605454550895865 absolute error = 2e-31 relative error = 1.8667839288498186730116732096086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -2.63 y[1] (analytic) = 1.0720784622387660958127129062998 y[1] (numeric) = 1.0720784622387660958127129063 absolute error = 2e-31 relative error = 1.8655350988242999212982401699560e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.62 y[1] (analytic) = 1.0728028628274355931068319365058 y[1] (numeric) = 1.0728028628274355931068319365059 absolute error = 1e-31 relative error = 9.3213770642300550091992433390508e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.61 y[1] (analytic) = 1.0735345437630570885469936238617 y[1] (numeric) = 1.0735345437630570885469936238618 absolute error = 1e-31 relative error = 9.3150239627567391049785376980016e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.6 y[1] (analytic) = 1.07427357821433388042821057017 y[1] (numeric) = 1.0742735782143338804282105701701 absolute error = 1e-31 relative error = 9.3086157965665318214747685796835e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.59 y[1] (analytic) = 1.0750200400853269605252786986446 y[1] (numeric) = 1.0750200400853269605252786986448 absolute error = 2e-31 relative error = 1.8604304342468398317272232340262e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.58 y[1] (analytic) = 1.0757740040228454817788775160744 y[1] (numeric) = 1.0757740040228454817788775160746 absolute error = 2e-31 relative error = 1.8591265382143658479282197554773e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.57 y[1] (analytic) = 1.0765355454239115014167458275085 y[1] (numeric) = 1.0765355454239115014167458275087 absolute error = 2e-31 relative error = 1.8578113918314256716340992333181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.56 y[1] (analytic) = 1.0773047404432997459904656610398 y[1] (numeric) = 1.07730474044329974599046566104 absolute error = 2e-31 relative error = 1.8564849154724973256275757424238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.55 y[1] (analytic) = 1.0780816660011531523106412395528 y[1] (numeric) = 1.078081666001153152310641239553 absolute error = 2e-31 relative error = 1.8551470292769645643121529877046e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.54 y[1] (analytic) = 1.0788663997906749458409128226 y[1] (numeric) = 1.0788663997906749458409128226003 absolute error = 3e-31 relative error = 2.7806964797328653865020405740424e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -6.667e+29 TOP MAIN SOLVE Loop x[1] = -2.53 y[1] (analytic) = 1.0796590202858980257650549064864 y[1] (numeric) = 1.0796590202858980257650549064867 absolute error = 3e-31 relative error = 2.7786550601926041464543635894306e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.52 y[1] (analytic) = 1.0804596067495324336721400015193 y[1] (numeric) = 1.0804596067495324336721400015196 absolute error = 3e-31 relative error = 2.7765961645019157888778578505918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop bytes used=48018984, alloc=4324584, time=1.81 x[1] = -2.51 y[1] (analytic) = 1.0812682392408916906131760818382 y[1] (numeric) = 1.0812682392408916906131760818385 absolute error = 3e-31 relative error = 2.7745196715536201611115060345220e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.5 y[1] (analytic) = 1.0820849986238987951695286744672 y[1] (numeric) = 1.0820849986238987951695286744675 absolute error = 3e-31 relative error = 2.7724254599362693464200814700612e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.49 y[1] (analytic) = 1.0829099665751726831396061170947 y[1] (numeric) = 1.082909966575172683139606117095 absolute error = 3e-31 relative error = 2.7703134079445635132467690216117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.48 y[1] (analytic) = 1.0837432255921959574965153919751 y[1] (numeric) = 1.0837432255921959574965153919754 absolute error = 3e-31 relative error = 2.7681833935900203525673755136366e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.47 y[1] (analytic) = 1.084584859001564705396490765854 y[1] (numeric) = 1.0845848590015647053964907658543 absolute error = 3e-31 relative error = 2.7660352946119008744595030653128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.46 y[1] (analytic) = 1.0854349509673212272266709492054 y[1] (numeric) = 1.0854349509673212272266709492057 absolute error = 3e-31 relative error = 2.7638689884883943143360813372525e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.45 y[1] (analytic) = 1.0862935864993705109720735165162 y[1] (numeric) = 1.0862935864993705109720735165165 absolute error = 3e-31 relative error = 2.7616843524480648767951299253734e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.44 y[1] (analytic) = 1.0871608514619812935562170370773 y[1] (numeric) = 1.0871608514619812935562170370776 absolute error = 3e-31 relative error = 2.7594812634815630206616438783167e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.43 y[1] (analytic) = 1.088036832582372559268609219894 y[1] (numeric) = 1.0880368325823725592686092198944 absolute error = 4e-31 relative error = 3.6763461311381386166638816184592e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.42 y[1] (analytic) = 1.0889216174593863339360992607368 y[1] (numeric) = 1.0889216174593863339360992607371 absolute error = 3e-31 relative error = 2.7550192336152160475900113377876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.41 y[1] (analytic) = 1.0898152945722476421247388791339 y[1] (numeric) = 1.0898152945722476421247388791342 absolute error = 3e-31 relative error = 2.7527600456162616071351496888123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.4 y[1] (analytic) = 1.0907179532894125033751722200797 y[1] (numeric) = 1.09071795328941250337517222008 absolute error = 3e-31 relative error = 2.7504819105182328880111426827184e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.39 y[1] (analytic) = 1.0916296838775048522785515142203 y[1] (numeric) = 1.0916296838775048522785515142206 absolute error = 3e-31 relative error = 2.7481847043073256070599405548770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.38 y[1] (analytic) = 1.092550577510343276092433546306 y[1] (numeric) = 1.0925505775103432760924335463063 absolute error = 3e-31 relative error = 2.7458683028077926452156372420223e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.37 y[1] (analytic) = 1.093480726278058472577940827977 y[1] (numeric) = 1.0934807262780584725779408279773 absolute error = 3e-31 relative error = 2.7435325816955803580079858349987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.36 y[1] (analytic) = 1.0944202231963023398115690978577 y[1] (numeric) = 1.094420223196302339811569097858 absolute error = 3e-31 relative error = 2.7411774165122499379290190912757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.35 y[1] (analytic) = 1.0953691622155496188882965967998 y[1] (numeric) = 1.0953691622155496188882965968001 absolute error = 3e-31 relative error = 2.7388026826791862208169934687480e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.34 y[1] (analytic) = 1.0963276382304930196880168239591 y[1] (numeric) = 1.0963276382304930196880168239594 absolute error = 3e-31 relative error = 2.7364082555120962827426217086384e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.33 y[1] (analytic) = 1.0972957470895327692257007145515 y[1] (numeric) = 1.0972957470895327692257007145518 absolute error = 3e-31 relative error = 2.7339940102358001258316278429119e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.32 y[1] (analytic) = 1.0982735856043615315480312388239 y[1] (numeric) = 1.0982735856043615315480312388241 absolute error = 2e-31 relative error = 1.8210398813328771339862620046121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.31 y[1] (analytic) = 1.0992612515596456576764875455719 y[1] (numeric) = 1.0992612515596456576764875455721 absolute error = 2e-31 relative error = 1.8194037105941603083082652417712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.3 y[1] (analytic) = 1.100258843722803733729940693798 y[1] (numeric) = 1.1002588437228037337299406937982 absolute error = 2e-31 relative error = 1.8177540779702877293213905060472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=52020548, alloc=4324584, time=1.96 TOP MAIN SOLVE Loop x[1] = -2.29 y[1] (analytic) = 1.1012664618538834050897220493467 y[1] (numeric) = 1.1012664618538834050897220493469 absolute error = 2e-31 relative error = 1.8160909001379913250964914295214e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.28 y[1] (analytic) = 1.1022842067155374642978115675971 y[1] (numeric) = 1.1022842067155374642978115675973 absolute error = 2e-31 relative error = 1.8144140937656859978275778047023e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.27 y[1] (analytic) = 1.1033121800831002003052492153345 y[1] (numeric) = 1.1033121800831002003052492153347 absolute error = 2e-31 relative error = 1.8127235755245286132668852783666e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.26 y[1] (analytic) = 1.1043504847547650167140913586396 y[1] (numeric) = 1.1043504847547650167140913586398 absolute error = 2e-31 relative error = 1.8110192620996814054656515775236e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.25 y[1] (analytic) = 1.1053992245618643367832176892407 y[1] (numeric) = 1.1053992245618643367832176892409 absolute error = 2e-31 relative error = 1.8093010702017810120607704735433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.24 y[1] (analytic) = 1.1064585043792528231970558860814 y[1] (numeric) = 1.1064585043792528231970558860816 absolute error = 2e-31 relative error = 1.8075689165786143076761213341228e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.23 y[1] (analytic) = 1.107528430135794950927853596553 y[1] (numeric) = 1.1075284301357949509278535965533 absolute error = 3e-31 relative error = 2.7087340770405032301804478828549e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.22 y[1] (analytic) = 1.1086091088249579819575236377746 y[1] (numeric) = 1.1086091088249579819575236377748 absolute error = 2e-31 relative error = 1.8040623914048921292654182773754e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.21 y[1] (analytic) = 1.1097006485155114011653621107986 y[1] (numeric) = 1.1097006485155114011653621107988 absolute error = 2e-31 relative error = 1.8022878536436612617575430166251e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.164e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = -2.2 y[1] (analytic) = 1.1108031583623338833341444258499 y[1] (numeric) = 1.1108031583623338833341444258502 absolute error = 3e-31 relative error = 2.7007485326409445590171919959011e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.19 y[1] (analytic) = 1.1119167486173288719803056840571 y[1] (numeric) = 1.1119167486173288719803056840574 absolute error = 3e-31 relative error = 2.6980437193076794218826190096989e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.18 y[1] (analytic) = 1.1130415306404498615751847797268 y[1] (numeric) = 1.113041530640449861575184779727 absolute error = 2e-31 relative error = 1.7968781442047267016861517007293e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.17 y[1] (analytic) = 1.1141776169108364856947421133822 y[1] (numeric) = 1.1141776169108364856947421133825 absolute error = 3e-31 relative error = 2.6925688996677079230926734391883e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.16 y[1] (analytic) = 1.1153251210380625247158459917298 y[1] (numeric) = 1.1153251210380625247158459917301 absolute error = 3e-31 relative error = 2.6897986456252512513525998130982e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.15 y[1] (analytic) = 1.1164841577734969578692707141828 y[1] (numeric) = 1.1164841577734969578692707141831 absolute error = 3e-31 relative error = 2.6870063306429961078902893425762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.000e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -2.14 y[1] (analytic) = 1.1176548430217791957640792206891 y[1] (numeric) = 1.1176548430217791957640792206893 absolute error = 2e-31 relative error = 1.7894612209549804400181830193304e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.13 y[1] (analytic) = 1.1188372938524096409162054647724 y[1] (numeric) = 1.1188372938524096409162054647727 absolute error = 3e-31 relative error = 2.6813550249744733222730054809633e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.12 y[1] (analytic) = 1.1200316285114567353469482026623 y[1] (numeric) = 1.1200316285114567353469482026626 absolute error = 3e-31 relative error = 2.6784957885404154750820745446828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.11 y[1] (analytic) = 1.1212379664333816659658919534078 y[1] (numeric) = 1.1212379664333816659658919534081 absolute error = 3e-31 relative error = 2.6756139997139893025369493771899e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.1 y[1] (analytic) = 1.1224564282529819102186473760726 y[1] (numeric) = 1.1224564282529819102186473760729 absolute error = 3e-31 relative error = 2.6727095364131611851026817827747e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.09 y[1] (analytic) = 1.12368713581745481636392882593 y[1] (numeric) = 1.1236871358174548163639288259303 absolute error = 3e-31 relative error = 2.6697822769124909658192606431407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.08 y[1] (analytic) = 1.1249302121985824247480498144888 y[1] (numeric) = 1.1249302121985824247480498144891 absolute error = 3e-31 relative error = 2.6668320998657772871804785469574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=56023096, alloc=4324584, time=2.11 TOP MAIN SOLVE Loop x[1] = -2.07 y[1] (analytic) = 1.1261857817050387485691178744718 y[1] (numeric) = 1.126185781705038748569117874472 absolute error = 2e-31 relative error = 1.7759059228860193809816504376858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.06 y[1] (analytic) = 1.1274539698948207448692613507224 y[1] (numeric) = 1.1274539698948207448692613507227 absolute error = 3e-31 relative error = 2.6608625097837630894894662380687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.05 y[1] (analytic) = 1.1287349035878042188623465167449 y[1] (numeric) = 1.1287349035878042188623465167452 absolute error = 3e-31 relative error = 2.6578428561606274312894481134833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.04 y[1] (analytic) = 1.1300287108784259171980810770711 y[1] (numeric) = 1.1300287108784259171980810770714 absolute error = 3e-31 relative error = 2.6547998038633505579818857335535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.03 y[1] (analytic) = 1.1313355211484930783823989120881 y[1] (numeric) = 1.1313355211484930783823989120884 absolute error = 3e-31 relative error = 2.6517332337930154754375131242788e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.02 y[1] (analytic) = 1.1326554650801217213198427647316 y[1] (numeric) = 1.1326554650801217213198427647319 absolute error = 3e-31 relative error = 2.6486430273726584292648101862469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2.01 y[1] (analytic) = 1.1339886746688049658175810503738 y[1] (numeric) = 1.133988674668804965817581050374 absolute error = 2e-31 relative error = 1.7636860443814609169319730755154e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 1.1353352832366126918939994949725 y[1] (numeric) = 1.1353352832366126918939994949727 absolute error = 2e-31 relative error = 1.7615941559557648881194582826048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 1.1366954254455238578687982134042 y[1] (numeric) = 1.1366954254455238578687982134044 absolute error = 2e-31 relative error = 1.7594862750644983785925444595802e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 1.1380692373108928104775135397954 y[1] (numeric) = 1.1380692373108928104775135397956 absolute error = 2e-31 relative error = 1.7573623242165262815174651731321e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 1.1394568562150509336526980245391 y[1] (numeric) = 1.1394568562150509336526980245394 absolute error = 3e-31 relative error = 2.6328333395308534017736772246951e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 1.140858420921044996147971461096 y[1] (numeric) = 1.1408584209210449961479714610962 absolute error = 2e-31 relative error = 1.7530659048695520171576446431400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 1.1422740715865135718511540088638 y[1] (numeric) = 1.1422740715865135718511540088641 absolute error = 3e-31 relative error = 2.6263399254377507352490813230460e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 1.1437039497777029204400764475696 y[1] (numeric) = 1.1437039497777029204400764475699 absolute error = 3e-31 relative error = 2.6230564304539630067823003454233e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 1.1451481984836237299808130836871 y[1] (numeric) = 1.1451481984836237299808130836874 absolute error = 3e-31 relative error = 2.6197482596335776402848303123988e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 1.146606962130350137154394456995 y[1] (numeric) = 1.1466069621303501371543944569953 absolute error = 3e-31 relative error = 2.6164153010427560151655703019250e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 1.1480803865954624550259384084542 y[1] (numeric) = 1.1480803865954624550259384084545 absolute error = 3e-31 relative error = 2.6130574435612929280835131511287e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 1.1495686192226350526410120691037 y[1] (numeric) = 1.149568619222635052641012069104 absolute error = 3e-31 relative error = 2.6096745769110064435340220267777e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 1.1510718088363708452493410130273 y[1] (numeric) = 1.1510718088363708452493410130276 absolute error = 3e-31 relative error = 2.6062665916844300019271900661084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 1.1525901057568838686171667280872 y[1] (numeric) = 1.1525901057568838686171667280875 absolute error = 3e-31 relative error = 2.6028333793738038402244150543297e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 1.154123661815131425698085826774 y[1] (numeric) = 1.1541236618151314256980858267743 absolute error = 3e-31 relative error = 2.5993748324003625872650483202893e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 1.1556726303679973088895649117416 y[1] (numeric) = 1.1556726303679973088895649117419 absolute error = 3e-31 relative error = 2.5958908441439156997115853200274e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=60027552, alloc=4324584, time=2.27 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 1.1572371663136276162100094749031 y[1] (numeric) = 1.1572371663136276162100094749034 absolute error = 3e-31 relative error = 2.5923813089727172051087604426918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 1.158817426106920694990784426392 y[1] (numeric) = 1.1588174261069206949907844263922 absolute error = 2e-31 relative error = 1.7258974148490806772882772549363e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 1.160413567775172762090463784878 y[1] (numeric) = 1.1604135677751727620904637848783 absolute error = 3e-31 relative error = 2.5852851804825178727454704478253e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 1.1620257509338807652063690145142 y[1] (numeric) = 1.1620257509338807652063690145145 absolute error = 3e-31 relative error = 2.5816983811150497657321562978113e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 1.1636541368027040655826962573359 y[1] (numeric) = 1.1636541368027040655826962573362 absolute error = 3e-31 relative error = 2.5780856227975974720035464158685e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 1.1652988882215865382968047204322 y[1] (numeric) = 1.1652988882215865382968047204325 absolute error = 3e-31 relative error = 2.5744468052985366312171656745872e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 1.1669601696670407023471299750829 y[1] (numeric) = 1.1669601696670407023471299750832 absolute error = 3e-31 relative error = 2.5707818295597575642954267198506e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 1.1686381472685955089693011128318 y[1] (numeric) = 1.1686381472685955089693011128321 absolute error = 3e-31 relative error = 2.5670905977284438194304650001746e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 1.1703329888254094329729999061631 y[1] (numeric) = 1.1703329888254094329729999061633 absolute error = 2e-31 relative error = 1.7089153421260694707999300265688e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 1.172044863823050528422539948626 y[1] (numeric) = 1.1720448638230505284225399486262 absolute error = 2e-31 relative error = 1.7064193203972352350446025870951e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 1.1737739434504451266807172586664 y[1] (numeric) = 1.1737739434504451266807172586666 absolute error = 2e-31 relative error = 1.7039056039366210605876302696313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 1.1755204006169968716998606943422 y[1] (numeric) = 1.1755204006169968716998606943424 absolute error = 2e-31 relative error = 1.7013741309383124985495717588231e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 1.1772844099698778044778771942594 y[1] (numeric) = 1.1772844099698778044778771942596 absolute error = 2e-31 relative error = 1.6988248405083121197567123724846e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 1.1790661479114932258021467343306 y[1] (numeric) = 1.1790661479114932258021467343308 absolute error = 2e-31 relative error = 1.6962576726866814386887615120147e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 1.1808657926171220837820954906518 y[1] (numeric) = 1.180865792617122083782095490652 absolute error = 2e-31 relative error = 1.6936725684698276493907668043585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 1.1826835240527346502239008377589 y[1] (numeric) = 1.1826835240527346502239008377591 absolute error = 2e-31 relative error = 1.6910694698329305913320924692172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 1.1845195239929892676298137659024 y[1] (numeric) = 1.1845195239929892676298137659026 absolute error = 2e-31 relative error = 1.6884483197525052016708467907492e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 1.1863739760394099665117959887401 y[1] (numeric) = 1.1863739760394099665117959887402 absolute error = 1e-31 relative error = 8.4290453111454727379837147735861e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 1.1882470656387467707963511700788 y[1] (numeric) = 1.1882470656387467707963511700789 absolute error = 1e-31 relative error = 8.4157582115504418423026188432352e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 1.1901389801015205273663910582943 y[1] (numeric) = 1.1901389801015205273663910582944 absolute error = 1e-31 relative error = 8.4023800305633094616936080902046e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 1.1920499086207541142385447911733 y[1] (numeric) = 1.1920499086207541142385447911734 absolute error = 1e-31 relative error = 8.3889105042341476280854740321649e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 1.1939800422908919005123384942873 y[1] (numeric) = 1.1939800422908919005123384942874 absolute error = 1e-31 relative error = 8.3753493741930392359826077916689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=64031128, alloc=4324584, time=2.41 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 1.1959295741269093500530063600373 y[1] (numeric) = 1.1959295741269093500530063600374 absolute error = 1e-31 relative error = 8.3616963877664108556345423708252e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 1.1978986990836146798842262112941 y[1] (numeric) = 1.1978986990836146798842262112942 absolute error = 1e-31 relative error = 8.3479512980938538647839133756685e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 1.1998876140751445034727035921351 y[1] (numeric) = 1.1998876140751445034727035921352 absolute error = 1e-31 relative error = 8.3341138642454035297561660810929e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 1.2018965179946554084851792676434 y[1] (numeric) = 1.2018965179946554084851792676435 absolute error = 1e-31 relative error = 8.3201838513392448184242232820009e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 1.2039256117342134381920455363505 y[1] (numeric) = 1.2039256117342134381920455363507 absolute error = 2e-31 relative error = 1.6612322061319625754688715943832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 1.2059750982048834654822863400384 y[1] (numeric) = 1.2059750982048834654822863400386 absolute error = 2e-31 relative error = 1.6584090359552510507363316680547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 1.2080451823570204684438838657276 y[1] (numeric) = 1.2080451823570204684438838657277 absolute error = 1e-31 relative error = 8.2778360826612220900083900369731e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 1.2101360712007647366541591331939 y[1] (numeric) = 1.2101360712007647366541591331941 absolute error = 2e-31 relative error = 1.6527067059619899334535068815247e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 1.2122479738267430577177549975797 y[1] (numeric) = 1.2122479738267430577177549975799 absolute error = 2e-31 relative error = 1.6498274636719203637531247958749e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 1.2143811014269779541881664116833 y[1] (numeric) = 1.2143811014269779541881664116835 absolute error = 2e-31 relative error = 1.6469294504417665773259866514364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 1.2165356673160070618139345231369 y[1] (numeric) = 1.2165356673160070618139345231371 absolute error = 2e-31 relative error = 1.6440126284275070084777217008171e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 1.2187118869522147610649287664188 y[1] (numeric) = 1.218711886952214761064928766419 absolute error = 2e-31 relative error = 1.6410769611853463891758055838315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 1.2209099779593781951196459967695 y[1] (numeric) = 1.2209099779593781951196459967697 absolute error = 2e-31 relative error = 1.6381224136957159744494134313909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 1.223130160148429828933280470764 y[1] (numeric) = 1.2231301601484298289332804707642 absolute error = 2e-31 relative error = 1.6351489523872873192144343573125e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 1.2253726555394387256606070068809 y[1] (numeric) = 1.2253726555394387256606070068811 absolute error = 2e-31 relative error = 1.6321565451609914970721586544819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 1.2276376883838127385796374057948 y[1] (numeric) = 1.227637688383812738579637405795 absolute error = 2e-31 relative error = 1.6291451614140354854061091790886e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 1.2299254851867238387537443843114 y[1] (numeric) = 1.2299254851867238387537443843117 absolute error = 3e-31 relative error = 2.4391721580958609140935767841844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 1.2322362747297588209837070706824 y[1] (numeric) = 1.2322362747297588209837070706827 absolute error = 3e-31 relative error = 2.4345980243585416607974714513758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 1.234570288093797653139148917061 y[1] (numeric) = 1.2345702880937976531391489170612 absolute error = 2e-31 relative error = 1.6199968679693740496788150699775e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 1.2369277586821217567233665275514 y[1] (numeric) = 1.2369277586821217567233665275516 absolute error = 2e-31 relative error = 1.6169093028770650208491339298285e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (analytic) = 1.2393089222437545295188628493952 y[1] (numeric) = 1.2393089222437545295188628493954 absolute error = 2e-31 relative error = 1.6138026315335671397790780710560e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (analytic) = 1.2417140168970364443852997809855 y[1] (numeric) = 1.2417140168970364443852997809857 absolute error = 2e-31 relative error = 1.6106768328168441813225068415122e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=68032864, alloc=4324584, time=2.57 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (analytic) = 1.2441432831534370817393959731224 y[1] (numeric) = 1.2441432831534370817393959731226 absolute error = 2e-31 relative error = 1.6075318872684417317346129442166e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 1.2465969639416064769398612398338 y[1] (numeric) = 1.246596963941606476939861239834 absolute error = 2e-31 relative error = 1.6043677771171634963086871831038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.39 y[1] (analytic) = 1.2490753046316681877321489284998 y[1] (numeric) = 1.2490753046316681877321489285001 absolute error = 3e-31 relative error = 2.4017767294539945895596279267559e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.38 y[1] (analytic) = 1.2515785530597565110800150148691 y[1] (numeric) = 1.2515785530597565110800150148694 absolute error = 3e-31 relative error = 2.3969730007484118788046064313120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.37 y[1] (analytic) = 1.2541069595528003031260148277283 y[1] (numeric) = 1.2541069595528003031260148277286 absolute error = 3e-31 relative error = 2.3921404607066087001925183866022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36 y[1] (analytic) = 1.2566607769535558806835867050428 y[1] (numeric) = 1.256660776953555880683586705043 absolute error = 2e-31 relative error = 1.5915193954318164548680118753423e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.35 y[1] (analytic) = 1.2592402606458915075717326107116 y[1] (numeric) = 1.2592402606458915075717326107118 absolute error = 2e-31 relative error = 1.5882592563981053420816363809006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = -1.34 y[1] (analytic) = 1.2618456685803259942619996555144 y[1] (numeric) = 1.2618456685803259942619996555146 absolute error = 2e-31 relative error = 1.5849798828807287814708995800400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (analytic) = 1.2644772612998239647190094577137 y[1] (numeric) = 1.264477261299823964719009457714 absolute error = 3e-31 relative error = 2.3725219043608100725283405076077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.32 y[1] (analytic) = 1.2671353019658503699827155236038 y[1] (numeric) = 1.2671353019658503699827155236041 absolute error = 3e-31 relative error = 2.3675451195667586174490720208987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.31 y[1] (analytic) = 1.2698200563846868539654590407689 y[1] (numeric) = 1.2698200563846868539654590407692 absolute error = 3e-31 relative error = 2.3625394676323824931201656257588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (analytic) = 1.2725317930340126031223331675634 y[1] (numeric) = 1.2725317930340126031223331675637 absolute error = 3e-31 relative error = 2.3575049491276758378062654167752e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -1.29 y[1] (analytic) = 1.2752707830897523381019736371362 y[1] (numeric) = 1.2752707830897523381019736371365 absolute error = 3e-31 relative error = 2.3524415675324562572258743084837e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.28 y[1] (analytic) = 1.2780373004531941321993141560141 y[1] (numeric) = 1.2780373004531941321993141560144 absolute error = 3e-31 relative error = 2.3473493292693374894090653315350e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.27 y[1] (analytic) = 1.2808316217783797684147501301548 y[1] (numeric) = 1.2808316217783797684147501301551 absolute error = 3e-31 relative error = 2.3422282437363848640226425417408e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.26 y[1] (analytic) = 1.2836540264997703741782420084759 y[1] (numeric) = 1.2836540264997703741782420084763 absolute error = 4e-31 relative error = 3.1161044311192487332104975687437e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.165e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.25 y[1] (analytic) = 1.2865047968601901003248854266478 y[1] (numeric) = 1.2865047968601901003248854266482 absolute error = 4e-31 relative error = 3.1091994446987645879980781906463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.24 y[1] (analytic) = 1.2893842179390506387131321849311 y[1] (numeric) = 1.2893842179390506387131321849314 absolute error = 3e-31 relative error = 2.3266920428072203951237890767539e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.23 y[1] (analytic) = 1.2922925776808594009609443919072 y[1] (numeric) = 1.2922925776808594009609443919075 absolute error = 3e-31 relative error = 2.3214557228083614127355177678531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.22 y[1] (analytic) = 1.2952301669240142091415122843203 y[1] (numeric) = 1.2952301669240142091415122843206 absolute error = 3e-31 relative error = 2.3161906482803512236204855533798e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.21 y[1] (analytic) = 1.298197279429887377931600950376 y[1] (numeric) = 1.2981972794298873779316009503763 absolute error = 3e-31 relative error = 2.3108968471398056394421585460387e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (analytic) = 1.3011942119122020966449776070832 y[1] (numeric) = 1.3011942119122020966449776070836 absolute error = 4e-31 relative error = 3.0740991339960705717236506098538e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 bytes used=72033932, alloc=4324584, time=2.72 TOP MAIN SOLVE Loop x[1] = -1.19 y[1] (analytic) = 1.3042212640667040488136031743295 y[1] (numeric) = 1.3042212640667040488136031743299 absolute error = 4e-31 relative error = 3.0669642569141711727966589411696e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18 y[1] (analytic) = 1.3072787386011312365032726969182 y[1] (numeric) = 1.3072787386011312365032726969186 absolute error = 4e-31 relative error = 3.0597912150550588419744506649077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.17 y[1] (analytic) = 1.3103669412654850063711111154575 y[1] (numeric) = 1.3103669412654850063711111154579 absolute error = 4e-31 relative error = 3.0525800629074217178001107520587e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.16 y[1] (analytic) = 1.313486180882605304592756074811 y[1] (numeric) = 1.3134861808826053045927560748114 absolute error = 4e-31 relative error = 3.0453308593716416790000581355376e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.15 y[1] (analytic) = 1.3166367693790532182101999524295 y[1] (numeric) = 1.3166367693790532182101999524299 absolute error = 4e-31 relative error = 3.0380436677964442983428774237018e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -1.14 y[1] (analytic) = 1.3198190218163038911801614276738 y[1] (numeric) = 1.3198190218163038911801614276742 absolute error = 4e-31 relative error = 3.0307185560148194361059923371987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.13 y[1] (analytic) = 1.3230332564222529344405856126403 y[1] (numeric) = 1.3230332564222529344405856126407 absolute error = 4e-31 relative error = 3.0233555963791882398242006182313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.12 y[1] (analytic) = 1.3262797946230394806625348237426 y[1] (numeric) = 1.3262797946230394806625348237429 absolute error = 3e-31 relative error = 2.2619661493468442187808136766506e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.11 y[1] (analytic) = 1.3295589610751890660194644838161 y[1] (numeric) = 1.3295589610751890660194644838165 absolute error = 4e-31 relative error = 3.0085164457582806350919220329429e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (analytic) = 1.3328710836980795532888469064313 y[1] (numeric) = 1.3328710836980795532888469064317 absolute error = 4e-31 relative error = 3.0010404223804704168399073696483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09 y[1] (analytic) = 1.336216493706733342905508150893 y[1] (numeric) = 1.3362164937067333429055081508934 absolute error = 4e-31 relative error = 2.9935268864282569040831623377999e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.08 y[1] (analytic) = 1.3395955256449391512151102152476 y[1] (numeric) = 1.339595525644939151215110215248 absolute error = 4e-31 relative error = 2.9859759333506486713562932623629e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -1.07 y[1] (analytic) = 1.3430085174187066681332054893988 y[1] (numeric) = 1.3430085174187066681332054893991 absolute error = 3e-31 relative error = 2.2337907474824278562746077164423e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.06 y[1] (analytic) = 1.3464558103300574397035083480901 y[1] (numeric) = 1.3464558103300574397035083480905 absolute error = 4e-31 relative error = 2.9707621812107430696159068365441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.05 y[1] (analytic) = 1.3499377491111553546717988735768 y[1] (numeric) = 1.3499377491111553546717988735772 absolute error = 4e-31 relative error = 2.9630995967286159751635825082572e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.04 y[1] (analytic) = 1.353454681958780148152558265309 y[1] (numeric) = 1.3534546819587801481525582653093 absolute error = 3e-31 relative error = 2.2165500182527469828981111784822e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.03 y[1] (analytic) = 1.3570069605691473697674306156514 y[1] (numeric) = 1.3570069605691473697674306156517 absolute error = 3e-31 relative error = 2.2107476875002606975868399217983e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02 y[1] (analytic) = 1.360594940173078298281341634654 y[1] (numeric) = 1.3605949401730782982813416346544 absolute error = 4e-31 relative error = 2.9398903978660752426461936532144e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -1.01 y[1] (analytic) = 1.3642189795715233197570462956374 y[1] (numeric) = 1.3642189795715233197570462956377 absolute error = 3e-31 relative error = 2.1990604477165726870998236132422e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 1.3678794411714423215955237701615 y[1] (numeric) = 1.3678794411714423215955237701618 absolute error = 3e-31 relative error = 2.1931757358900146377534777254654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 1.3715766910220456905315241199082 y[1] (numeric) = 1.3715766910220456905315241199085 absolute error = 3e-31 relative error = 2.1872637670479194953604281562358e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 1.3753110988513995387142672324775 y[1] (numeric) = 1.3753110988513995387142672324778 absolute error = 3e-31 relative error = 2.1813246490233885977377796717952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=76034676, alloc=4324584, time=2.87 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 1.3790830381033988184264065277403 y[1] (numeric) = 1.3790830381033988184264065277406 absolute error = 3e-31 relative error = 2.1753584933694692444848625431972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 1.3828928859751120227835403627544 y[1] (numeric) = 1.3828928859751120227835403627548 absolute error = 4e-31 relative error = 2.8924872204975593142523721965663e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 1.386741023454501206915461774036 y[1] (numeric) = 1.3867410234545012069154617740363 absolute error = 3e-31 relative error = 2.1633455340685892752958905919581e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = 1.3906278353585211016626981379217 y[1] (numeric) = 1.390627835358521101662698137922 absolute error = 3e-31 relative error = 2.1572989722491516185230304293178e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = 1.3945537103716011297314597702349 y[1] (numeric) = 1.3945537103716011297314597702353 absolute error = 4e-31 relative error = 2.8683011419718901004058204815604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = 1.3985190410845141725406814138044 y[1] (numeric) = 1.3985190410845141725406814138048 absolute error = 4e-31 relative error = 2.8601684228039589719248860642473e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 1.4025242240336359746702320649927 y[1] (numeric) = 1.4025242240336359746702320649931 absolute error = 4e-31 relative error = 2.8520006510091266547301871460528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 1.4065696597405991118834542396456 y[1] (numeric) = 1.406569659740599111883454239646 absolute error = 4e-31 relative error = 2.8437980105000158538523929472014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = 1.4106557527523454881538800158902 y[1] (numeric) = 1.4106557527523454881538800158906 absolute error = 4e-31 relative error = 2.8355606902644797129023559514432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = 1.4147829116815813669792037174992 y[1] (numeric) = 1.4147829116815813669792037174997 absolute error = 5e-31 relative error = 3.5341111054678379004528746687791e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 1.4189515492476389825193552735605 y[1] (numeric) = 1.418951549247638982519355273561 absolute error = 5e-31 relative error = 3.5237284899904552428550183710825e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = 1.4231620823177488167538395179062 y[1] (numeric) = 1.4231620823177488167538395179067 absolute error = 5e-31 relative error = 3.5133032717236574340605673377709e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = 1.4274149319487266699204508411764 y[1] (numeric) = 1.4274149319487266699204508411768 absolute error = 4e-31 relative error = 2.8022685698958918004059510801443e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = 1.4317105234290796929771464081439 y[1] (numeric) = 1.4317105234290796929771464081443 absolute error = 4e-31 relative error = 2.7938608640101551018981074122370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = 1.4360492863215355927254126049699 y[1] (numeric) = 1.4360492863215355927254126049703 absolute error = 4e-31 relative error = 2.7854197192953365108718988476479e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 1.4404316545059992625510781754405 y[1] (numeric) = 1.4404316545059992625510781754409 absolute error = 4e-31 relative error = 2.7769453604321220335225348133170e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = 1.4448580662229411344814454391058 y[1] (numeric) = 1.4448580662229411344814454391062 absolute error = 4e-31 relative error = 2.7684380172071526420106333269745e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 1.4493289641172215914301023850156 y[1] (numeric) = 1.449328964117221591430102385016 absolute error = 4e-31 relative error = 2.7598979245104497705354962477937e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 1.4538447952823558221071605875315 y[1] (numeric) = 1.4538447952823558221071605875319 absolute error = 4e-31 relative error = 2.7513253223313615651310838932204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = 1.4584060113052235451172974700586 y[1] (numeric) = 1.4584060113052235451172974700591 absolute error = 5e-31 relative error = 3.4284005696912692058539990097913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 1.4630130683112280732552709485309 y[1] (numeric) = 1.4630130683112280732552709485314 absolute error = 5e-31 relative error = 3.4176044686815781375259926599884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = 1.4676664270099092339429686851366 y[1] (numeric) = 1.4676664270099092339429686851371 absolute error = 5e-31 relative error = 3.4067686689451277693291860606138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=80035416, alloc=4324584, time=3.02 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = 1.4723665527410147071380465509433 y[1] (numeric) = 1.4723665527410147071380465509438 absolute error = 5e-31 relative error = 3.3958934958769648657984005788828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = 1.4771139155210343878863400708347 y[1] (numeric) = 1.4771139155210343878863400708352 absolute error = 5e-31 relative error = 3.3849792811926149867837799399296e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = 1.4819089900902024269930828566272 y[1] (numeric) = 1.4819089900902024269930828566276 absolute error = 4e-31 relative error = 2.6992210903292540972177960473861e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = 1.4867522559599716500561676479956 y[1] (numeric) = 1.4867522559599716500561676479961 absolute error = 5e-31 relative error = 3.3630350853388022336852116897145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = 1.4916441974609651023429154350493 y[1] (numeric) = 1.4916441974609651023429154350498 absolute error = 5e-31 relative error = 3.3520057990443429478172524433917e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = 1.4965853037914095147048000933975 y[1] (numeric) = 1.496585303791409514704800093398 absolute error = 5e-31 relative error = 3.3409388608408305326539416481494e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.69 y[1] (analytic) = 1.5015760690660555339170813603031 y[1] (numeric) = 1.5015760690660555339170813603036 absolute error = 5e-31 relative error = 3.3298346337591012816090994160151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.68 y[1] (analytic) = 1.5066169923655896095071471097274 y[1] (numeric) = 1.5066169923655896095071471097279 absolute error = 5e-31 relative error = 3.3186934870217633547078706720491e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = 1.511708577786542478301424470106 y[1] (numeric) = 1.5117085777865424783014244701065 absolute error = 5e-31 relative error = 3.3075157960147621288394927684670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = 1.5168513344916992375809050183918 y[1] (numeric) = 1.5168513344916992375809050183923 absolute error = 5e-31 relative error = 3.2963019422569271038105653567629e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = 1.5220457767610160478946081372088 y[1] (numeric) = 1.5220457767610160478946081372094 absolute error = 6e-31 relative error = 3.9420627760409927155993999334121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (analytic) = 1.5272924240430485572436946085663 y[1] (numeric) = 1.5272924240430485572436946085669 absolute error = 6e-31 relative error = 3.9285207636379153865451835321759e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -0.63 y[1] (analytic) = 1.532591801006897189521506018502 y[1] (numeric) = 1.5325918010068971895215060185026 absolute error = 6e-31 relative error = 3.9149367731564668204243033351001e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = 1.5379444375946744917816618612558 y[1] (numeric) = 1.5379444375946744917816618612565 absolute error = 7e-31 relative error = 4.5515298400167894398118278847267e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = 1.5433508690744997871126640878166 y[1] (numeric) = 1.5433508690744997871126640878172 absolute error = 6e-31 relative error = 3.8876448124839014096543048938396e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = 1.5488116360940264326284589172326 y[1] (numeric) = 1.5488116360940264326284589172332 absolute error = 6e-31 relative error = 3.8739378373547727174546638184712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (analytic) = 1.5543272847345070353453611638809 y[1] (numeric) = 1.5543272847345070353453611638815 absolute error = 6e-31 relative error = 3.8601908741664105313027572711356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = 1.5598983665654020325119832698729 y[1] (numeric) = 1.5598983665654020325119832698735 absolute error = 6e-31 relative error = 3.8464044380089023779941916036131e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (analytic) = 1.5655254386995370972957093374648 y[1] (numeric) = 1.5655254386995370972957093374654 absolute error = 6e-31 relative error = 3.8325790508930515222850885855157e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = 1.5712090638488148856122474668313 y[1] (numeric) = 1.5712090638488148856122474668319 absolute error = 6e-31 relative error = 3.8187152416893980574879535613013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = 1.5769498103804866953193699648816 y[1] (numeric) = 1.5769498103804866953193699648822 absolute error = 6e-31 relative error = 3.8048135460648040964293145543671e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = 1.5827482523739896649876540047778 y[1] (numeric) = 1.5827482523739896649876540047784 absolute error = 6e-31 relative error = 3.7908745064166099065355428547100e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=84036500, alloc=4324584, time=3.17 x[1] = -0.53 y[1] (analytic) = 1.5886049696783551960154643004118 y[1] (numeric) = 1.5886049696783551960154643004124 absolute error = 6e-31 relative error = 3.7768986718043692340720610819636e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = 1.5945205479701943389782298053389 y[1] (numeric) = 1.5945205479701943389782298053395 absolute error = 6e-31 relative error = 3.7628865978791734720246130921549e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.51 y[1] (analytic) = 1.6004955788122659427989706801995 y[1] (numeric) = 1.6004955788122659427989706802001 absolute error = 6e-31 relative error = 3.7488388468105757426178916162339e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (analytic) = 1.6065306597126334236037995349912 y[1] (numeric) = 1.6065306597126334236037995349918 absolute error = 6e-31 relative error = 3.7347559872111273878334033944730e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (analytic) = 1.612626394184416068988579968019 y[1] (numeric) = 1.6126263941844160689885799680197 absolute error = 7e-31 relative error = 4.3407450264016309196966308971522e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (analytic) = 1.6187833918061408528769619869106 y[1] (numeric) = 1.6187833918061408528769619869112 absolute error = 6e-31 relative error = 3.7064872486154938614782967810314e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (analytic) = 1.6250022682827007962015734619291 y[1] (numeric) = 1.6250022682827007962015734619298 absolute error = 7e-31 relative error = 4.3076862947382751927893824650320e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (analytic) = 1.6312836455069259692952345339618 y[1] (numeric) = 1.6312836455069259692952345339624 absolute error = 6e-31 relative error = 3.6780850568360128243749335188611e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = 1.6376281516217732931437434383122 y[1] (numeric) = 1.6376281516217732931437434383129 absolute error = 7e-31 relative error = 4.2744746376445539180843846311258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (analytic) = 1.644036421083141358532184030009 y[1] (numeric) = 1.6440364210831413585321840300096 absolute error = 6e-31 relative error = 3.6495541844790864928567125537860e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = 1.6505090947233165446190154984879 y[1] (numeric) = 1.6505090947233165446190154984885 absolute error = 6e-31 relative error = 3.6352420105905634652902743048829e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (analytic) = 1.65704681981505678160267362234 y[1] (numeric) = 1.6570468198150567816026736223406 absolute error = 6e-31 relative error = 3.6208994991883577597844592913272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = 1.6636502501363193659103535378148 y[1] (numeric) = 1.6636502501363193659103535378154 absolute error = 6e-31 relative error = 3.6065272730902186255758654482618e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (analytic) = 1.6703200460356393007444329251478 y[1] (numeric) = 1.6703200460356393007444329251485 absolute error = 7e-31 relative error = 4.1908136207871640025835506158386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = 1.6770568744981646998750723870924 y[1] (numeric) = 1.6770568744981646998750723870931 absolute error = 7e-31 relative error = 4.1739788950775148585979461263099e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = 1.6838614092123558582744019662858 y[1] (numeric) = 1.6838614092123558582744019662865 absolute error = 7e-31 relative error = 4.1571117205389989269849494069695e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (analytic) = 1.6907343306373546595549399642394 y[1] (numeric) = 1.6907343306373546595549399642402 absolute error = 8e-31 relative error = 4.7316718274622405716941366124194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = 1.6976763260710310572091292638382 y[1] (numeric) = 1.6976763260710310572091292638389 absolute error = 7e-31 relative error = 4.1232830384106556991648950986231e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = 1.7046880897187134343548206990309 y[1] (numeric) = 1.7046880897187134343548206990316 absolute error = 7e-31 relative error = 4.1063230524213104045592410826380e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (analytic) = 1.711770322762609715079953510757 y[1] (numeric) = 1.7117703227626097150799535107577 absolute error = 7e-31 relative error = 4.0893336605478514787936250112632e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = 1.7189237334319261695554184761104 y[1] (numeric) = 1.7189237334319261695554184761111 absolute error = 7e-31 relative error = 4.0723156378928536821268667251349e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = 1.7261490370736909248550475294236 y[1] (numeric) = 1.7261490370736909248550475294243 absolute error = 7e-31 relative error = 4.0552697650412462156808533297639e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop bytes used=88037288, alloc=4324584, time=3.32 x[1] = -0.31 y[1] (analytic) = 1.7334469562242892638928316633154 y[1] (numeric) = 1.7334469562242892638928316633162 absolute error = 8e-31 relative error = 4.6150820890563706614167401387659e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = 1.7408182206817178660668737793178 y[1] (numeric) = 1.7408182206817178660668737793186 absolute error = 8e-31 relative error = 4.5955401344932718972165701218773e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = 1.7482635675785652150943529512748 y[1] (numeric) = 1.7482635675785652150943529512756 absolute error = 8e-31 relative error = 4.5759690634521490743498989489082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (analytic) = 1.7557837414557254721391008071943 y[1] (numeric) = 1.7557837414557254721391008071951 absolute error = 8e-31 relative error = 4.5563697915138321271890753563099e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (analytic) = 1.7633794943368531856805312195579 y[1] (numeric) = 1.7633794943368531856805312195587 absolute error = 8e-31 relative error = 4.5367432397236346602794734184191e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (analytic) = 1.7710515858035662836569559954336 y[1] (numeric) = 1.7710515858035662836569559954344 absolute error = 8e-31 relative error = 4.5170903344242333331154565428813e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (analytic) = 1.7788007830714048682451702669783 y[1] (numeric) = 1.7788007830714048682451702669791 absolute error = 8e-31 relative error = 4.4974120070863848322185891032236e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = 1.7866278610665534092190847475156 y[1] (numeric) = 1.7866278610665534092190847475164 absolute error = 8e-31 relative error = 4.4777091941375435584559631319064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (analytic) = 1.7945336025033340081706760906637 y[1] (numeric) = 1.7945336025033340081706760906645 absolute error = 8e-31 relative error = 4.4579828367884446169335040626583e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = 1.8025187979624784829842553829934 y[1] (numeric) = 1.8025187979624784829842553829942 absolute error = 8e-31 relative error = 4.4382338808577181163358148443138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (analytic) = 1.8105842459701870998377291515507 y[1] (numeric) = 1.8105842459701870998377291515515 absolute error = 8e-31 relative error = 4.4184632765946021627627566353813e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (analytic) = 1.818730753077981858669935508619 y[1] (numeric) = 1.8187307530779818586699355086198 absolute error = 8e-31 relative error = 4.3986719784998232684732203347135e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = 1.8269591339433623175091467937083 y[1] (numeric) = 1.8269591339433623175091467937091 absolute error = 8e-31 relative error = 4.3788609451447141870676915211930e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = 1.8352702114112720213123849740188 y[1] (numeric) = 1.8352702114112720213123849740195 absolute error = 7e-31 relative error = 3.8141522466150603781262212503641e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (analytic) = 1.8436648165963836820263226519154 y[1] (numeric) = 1.8436648165963836820263226519161 absolute error = 7e-31 relative error = 3.7967855854204569431358508415381e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (analytic) = 1.8521437889662113384563469814686 y[1] (numeric) = 1.8521437889662113384563469814692 absolute error = 6e-31 relative error = 3.2394893073333940855170672751515e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (analytic) = 1.8607079764250578072290337645433 y[1] (numeric) = 1.8607079764250578072290337645439 absolute error = 6e-31 relative error = 3.2245790720624972966700941621545e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = 1.8693582353988058196630844161712 y[1] (numeric) = 1.8693582353988058196630844161718 absolute error = 6e-31 relative error = 3.2096576709492869576703488962507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = 1.8780954309205613237330724091574 y[1] (numeric) = 1.878095430920561323733072409158 absolute error = 6e-31 relative error = 3.1947258383239125145564566046392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = 1.8869204367171575155275652287698 y[1] (numeric) = 1.8869204367171575155275652287704 absolute error = 6e-31 relative error = 3.1797843105874305046244072327248e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.11 y[1] (analytic) = 1.8958341352965282506768545828765 y[1] (numeric) = 1.8958341352965282506768545828771 absolute error = 6e-31 relative error = 3.1648338260675622669243947862593e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = 1.9048374180359595731642490594464 y[1] (numeric) = 1.904837418035959573164249059447 absolute error = 6e-31 relative error = 3.1498751248736399165951590956249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=92038336, alloc=4324584, time=3.48 x[1] = -0.09 y[1] (analytic) = 1.9139311852712281867473535464995 y[1] (numeric) = 1.9139311852712281867473535465001 absolute error = 6e-31 relative error = 3.1349089487508007401072092507920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = 1.9231163463866357829107598495724 y[1] (numeric) = 1.923116346386635782910759849573 absolute error = 6e-31 relative error = 3.1199360409334907115298282267535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = 1.932393819905948228857972632485 y[1] (numeric) = 1.9323938199059482288579726324856 absolute error = 6e-31 relative error = 3.1049571459983383298655127000324e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (analytic) = 1.9417645335842487095371527832712 y[1] (numeric) = 1.9417645335842487095371527832718 absolute error = 6e-31 relative error = 3.0899730097164604337577145009711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (analytic) = 1.9512294245007140090914253197796 y[1] (numeric) = 1.9512294245007140090914253197803 absolute error = 7e-31 relative error = 3.5874817753894724056305093249062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (analytic) = 1.9607894391523232094392106913232 y[1] (numeric) = 1.9607894391523232094392106913239 absolute error = 7e-31 relative error = 3.5699906681597582614059935415526e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = 1.9704455335485081769325283519592 y[1] (numeric) = 1.9704455335485081769325283519599 absolute error = 7e-31 relative error = 3.5524960628543427295048098225841e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (analytic) = 1.9801986733067553022208141042253 y[1] (numeric) = 1.980198673306755302220814104226 absolute error = 7e-31 relative error = 3.5349988333799981111876512189810e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (analytic) = 1.99004983374916805357390597718 y[1] (numeric) = 1.9900498337491680535739059771807 absolute error = 7e-31 relative error = 3.5174998541681249852432050524977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2.0000000000000000000000000000007 absolute error = 7e-31 relative error = 3.5000000000000000000000000000000e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 2.0100501670841680575421654569029 y[1] (numeric) = 2.0100501670841680575421654569036 absolute error = 7e-31 relative error = 3.4825001458318750147567949475023e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 2.0202013400267558101601439204832 y[1] (numeric) = 2.0202013400267558101601439204839 absolute error = 7e-31 relative error = 3.4650011666200018888123487810190e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 2.0304545339535168556124399538312 y[1] (numeric) = 2.0304545339535168556124399538319 absolute error = 7e-31 relative error = 3.4475039371456572704951901774159e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 2.0408107741923882267570447579169 y[1] (numeric) = 2.0408107741923882267570447579176 absolute error = 7e-31 relative error = 3.4300093318402417385940064584474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 2.0512710963760240396975176363356 y[1] (numeric) = 2.0512710963760240396975176363364 absolute error = 8e-31 relative error = 3.9000208281263172507079893429645e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 2.0618365465453596222246848771684 y[1] (numeric) = 2.0618365465453596222246848771691 absolute error = 7e-31 relative error = 3.3950314886641294939493330822003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 2.0725081812542164790531039498891 y[1] (numeric) = 2.0725081812542164790531039498898 absolute error = 7e-31 relative error = 3.3775499963352719484902351832955e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 2.0832870676749585544359877586749 y[1] (numeric) = 2.0832870676749585544359877586756 absolute error = 7e-31 relative error = 3.3600746189109275032152004021209e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 2.0941742837052103578728976235449 y[1] (numeric) = 2.0941742837052103578728976235456 absolute error = 7e-31 relative error = 3.3426062264573991365415892074093e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 2.1051709180756476248117078264902 y[1] (numeric) = 2.105170918075647624811707826491 absolute error = 8e-31 relative error = 3.8001665001684801112064545391669e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 2.116278070458871291500737769053 y[1] (numeric) = 2.1162780704588712915007377690537 absolute error = 7e-31 relative error = 3.3076938695878440219215394160308e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 2.1274968515793756714792655693748 y[1] (numeric) = 2.1274968515793756714792655693756 absolute error = 8e-31 relative error = 3.7602875858834259938341236897004e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=96039144, alloc=4390108, time=3.63 x[1] = 0.13 y[1] (analytic) = 2.138828383324621830615712602619 y[1] (numeric) = 2.1388283833246218306157126026197 absolute error = 7e-31 relative error = 3.2728198552887687330174672945876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 2.1502737988572272681235642576211 y[1] (numeric) = 2.1502737988572272681235642576219 absolute error = 8e-31 relative error = 3.7204564387342840564395348049991e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 2.1618342427282831226166202143317 y[1] (numeric) = 2.1618342427282831226166202143324 absolute error = 7e-31 relative error = 3.2379910825937531538848901441530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 2.173510870991810235018611086892 y[1] (numeric) = 2.1735108709918102350186110868927 absolute error = 7e-31 relative error = 3.2205958081110402335634215123232e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 2.1853048513203655140288527643693 y[1] (numeric) = 2.18530485132036551402885276437 absolute error = 7e-31 relative error = 3.2032144145795430568641491584619e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 2.1972173631218101648768239736005 y[1] (numeric) = 2.1972173631218101648768239736012 absolute error = 7e-31 relative error = 3.1858477533849396218737787496358e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 2.2092495976572514582858497035543 y[1] (numeric) = 2.209249597657251458285849703555 absolute error = 7e-31 relative error = 3.1684966729983750863157699189562e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 2.2214027581601698339210719946397 y[1] (numeric) = 2.2214027581601698339210719946404 absolute error = 7e-31 relative error = 3.1511620188126546400859322071257e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 2.2336780599567432511313258071563 y[1] (numeric) = 2.233678059956743251131325807157 absolute error = 7e-31 relative error = 3.1338446329797231075825879440414e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 2.2460767305873808195202647829927 y[1] (numeric) = 2.2460767305873808195202647829934 absolute error = 7e-31 relative error = 3.1165453542494966482061620112254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 2.258600009929477862811072376219 y[1] (numeric) = 2.2586000099294778628110723762197 absolute error = 7e-31 relative error = 3.0992650178101109601831839451739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.000e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 2.2712491503214046916134410512278 y[1] (numeric) = 2.2712491503214046916134410512285 absolute error = 7e-31 relative error = 3.0820044551296493863510322595819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 2.2840254166877414840734205680624 y[1] (numeric) = 2.2840254166877414840734205680632 absolute error = 8e-31 relative error = 3.5025879929136151677814108967765e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 2.2969300866657717979985630881788 y[1] (numeric) = 2.2969300866657717979985630881796 absolute error = 8e-31 relative error = 3.4829096655757666668845434571187e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 2.3099644507332473639149892266262 y[1] (numeric) = 2.309964450733247363914989226627 absolute error = 8e-31 relative error = 3.4632567602763653397205265815810e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 2.3231298123374369356421517730364 y[1] (numeric) = 2.3231298123374369356421517730372 absolute error = 8e-31 relative error = 3.4436302084861678728109246436902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 2.3364274880254721033778956250755 y[1] (numeric) = 2.3364274880254721033778956250763 absolute error = 8e-31 relative error = 3.4240309365478509256501010510918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 2.349858807576003103983744313328 y[1] (numeric) = 2.3498588075760031039837443133288 absolute error = 8e-31 relative error = 3.4044598655067281027834298781228e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 2.3634251141321777941611551872143 y[1] (numeric) = 2.3634251141321777941611551872151 absolute error = 8e-31 relative error = 3.3849179109436293385832598612343e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 2.3771277643359570845268770678281 y[1] (numeric) = 2.3771277643359570845268770678289 absolute error = 8e-31 relative error = 3.3654059828100043249361676231270e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 2.3909681284637802662427478049531 y[1] (numeric) = 2.3909681284637802662427478049539 absolute error = 8e-31 relative error = 3.3459249852653100775692951712745e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 2.4049475905635937968456495337223 y[1] (numeric) = 2.404947590563593796845649533723 absolute error = 7e-31 relative error = 2.9106663394521485212063749887367e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=100039828, alloc=4390108, time=3.78 x[1] = 0.35 y[1] (analytic) = 2.4190675485932572482703956619399 y[1] (numeric) = 2.4190675485932572482703956619406 absolute error = 7e-31 relative error = 2.8936769475786895954407589173619e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 2.4333294145603402577756905512456 y[1] (numeric) = 2.4333294145603402577756905512463 absolute error = 7e-31 relative error = 2.8767169615893443008351049013768e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 2.4477346146633244615847523355192 y[1] (numeric) = 2.4477346146633244615847523355199 absolute error = 7e-31 relative error = 2.8597871509705394997676304641332e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 2.46228458943422453155163160907 y[1] (numeric) = 2.4622845894342245315516316090707 absolute error = 7e-31 relative error = 2.8428882794610010730150505930305e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 2.4769807938826425770757438765387 y[1] (numeric) = 2.4769807938826425770757438765394 absolute error = 7e-31 relative error = 2.8260211049224851414020538736901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 2.4918246976412703178248529528372 y[1] (numeric) = 2.4918246976412703178248529528379 absolute error = 7e-31 relative error = 2.8091863792128359974164493841615e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 2.5068177851128535776050298262424 y[1] (numeric) = 2.5068177851128535776050298262431 absolute error = 7e-31 relative error = 2.7923848480614116034948236436945e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 2.5219615556186337959494448003237 y[1] (numeric) = 2.5219615556186337959494448003244 absolute error = 7e-31 relative error = 2.7756172509469159469181308267848e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 2.5372575235482814017008534659144 y[1] (numeric) = 2.5372575235482814017008534659151 absolute error = 7e-31 relative error = 2.7588843209776759571613466443033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 2.5527072185113360420500796461917 y[1] (numeric) = 2.5527072185113360420500796461924 absolute error = 7e-31 relative error = 2.7421867847743990916671686872495e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 2.5683121854901688111795997746932 y[1] (numeric) = 2.5683121854901688111795997746939 absolute error = 7e-31 relative error = 2.7255253623554460819156153688743e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 2.5840739849944817748625620134736 y[1] (numeric) = 2.5840739849944817748625620134743 absolute error = 7e-31 relative error = 2.7089007670246517048959108946619e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 2.5999941932173602410984500463115 y[1] (numeric) = 2.5999941932173602410984500463121 absolute error = 6e-31 relative error = 2.3076974616529069776091007442583e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.165e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 2.616074402192893382142499105688 y[1] (numeric) = 2.6160744021928933821424991056886 absolute error = 6e-31 relative error = 2.2935127513845061385217032189685e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 2.6323162199553789701224181313345 y[1] (numeric) = 2.6323162199553789701224181313351 absolute error = 6e-31 relative error = 2.2793614059414592116886020881554e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 2.6487212707001281468486507878142 y[1] (numeric) = 2.6487212707001281468486507878148 absolute error = 6e-31 relative error = 2.2652440127888726121665966055269e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 2.6652911949458863084291607887622 y[1] (numeric) = 2.6652911949458863084291607887629 absolute error = 7e-31 relative error = 2.6263546787209949669457931143939e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 2.6820276496988863469125541946667 y[1] (numeric) = 2.6820276496988863469125541946673 absolute error = 6e-31 relative error = 2.2371134021208265279753869078450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 2.6989323086185506544204144868253 y[1] (numeric) = 2.698932308618550654420414486826 absolute error = 7e-31 relative error = 2.5936182162282358935825954043757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 2.716006862184858460107349114715 y[1] (numeric) = 2.7160068621848584601073491147157 absolute error = 7e-31 relative error = 2.5773130758472884423752000028383e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 2.7332530178673952368219167671373 y[1] (numeric) = 2.733253017867395236821916767138 absolute error = 7e-31 relative error = 2.5610508629243952208324663532384e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 2.7506725002961010825499764350019 y[1] (numeric) = 2.7506725002961010825499764350025 absolute error = 6e-31 relative error = 2.1812847583106019425120464386986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop bytes used=104041152, alloc=4390108, time=3.94 x[1] = 0.57 y[1] (analytic) = 2.7682670514337351516208933928238 y[1] (numeric) = 2.7682670514337351516208933928245 absolute error = 7e-31 relative error = 2.5286577739581065573340633168984e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 2.7860384307500733822634435579423 y[1] (numeric) = 2.786038430750073382263443557943 absolute error = 7e-31 relative error = 2.5125281556562805590067764624513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 2.8039884153978569404293370747409 y[1] (numeric) = 2.8039884153978569404293370747416 absolute error = 7e-31 relative error = 2.4964439801391877134801165170084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 2.8221188003905089748753676681629 y[1] (numeric) = 2.8221188003905089748753676681636 absolute error = 7e-31 relative error = 2.4804058564194318296362255451168e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 2.8404313987816374553277937710156 y[1] (numeric) = 2.8404313987816374553277937710164 absolute error = 8e-31 relative error = 2.8164735833547981204609268082138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 2.8589280418463420441623540602681 y[1] (numeric) = 2.8589280418463420441623540602688 absolute error = 7e-31 relative error = 2.4484701599832105601881721152734e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 2.8776105792643431324381749672586 y[1] (numeric) = 2.8776105792643431324381749672593 absolute error = 7e-31 relative error = 2.4325737646507887095049794423831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 2.8964808793049513533417815912859 y[1] (numeric) = 2.8964808793049513533417815912866 absolute error = 7e-31 relative error = 2.4167257757557653823639525457948e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 2.9155408290138960701466981926821 y[1] (numeric) = 2.9155408290138960701466981926828 absolute error = 7e-31 relative error = 2.4009267612855084984673667443527e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 2.9347923344020315216931251510197 y[1] (numeric) = 2.9347923344020315216931251510204 absolute error = 7e-31 relative error = 2.3851772808403020546652085005318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 2.9542373206359394961594960015662 y[1] (numeric) = 2.9542373206359394961594960015669 absolute error = 7e-31 relative error = 2.3694778855793330196247101241461e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 2.9738777322304475935521277966183 y[1] (numeric) = 2.973877732230447593552127796619 absolute error = 7e-31 relative error = 2.3538291181695313034089810591313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 2.9937155332430823288996461769344 y[1] (numeric) = 2.9937155332430823288996461769351 absolute error = 7e-31 relative error = 2.3382315127372582057472608175789e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 3.0137527074704765216245493885831 y[1] (numeric) = 3.0137527074704765216245493885838 absolute error = 7e-31 relative error = 2.3226855948228372542844816925909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 3.0339912586467506119945217716624 y[1] (numeric) = 3.0339912586467506119945217716632 absolute error = 8e-31 relative error = 2.6367907215290512834923960905733e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 3.0544332106438877429504601670086 y[1] (numeric) = 3.0544332106438877429504601670093 absolute error = 7e-31 relative error = 2.2917508805256768728407036343998e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 3.0750806076741226449863758349892 y[1] (numeric) = 3.07508060767412264498637583499 absolute error = 8e-31 relative error = 2.6015578193414918055644079052276e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 3.0959355144943645631383178428338 y[1] (numeric) = 3.0959355144943645631383178428345 absolute error = 7e-31 relative error = 2.2610290063303390185027080840986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 3.1170000166126746685453698198371 y[1] (numeric) = 3.1170000166126746685453698198378 absolute error = 7e-31 relative error = 2.2457491057722491878822391895639e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 3.138276220496818602495941263298 y[1] (numeric) = 3.1382762204968186024959412632987 absolute error = 7e-31 relative error = 2.2305238634768211229391395151407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 3.15976625378491500838755239034 y[1] (numeric) = 3.1597662537849150083875523903408 absolute error = 8e-31 relative error = 2.5318328501094749799584117440186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 3.181472265498201116628849542537 y[1] (numeric) = 3.1814722654982011166288495425378 absolute error = 8e-31 relative error = 2.5145590884939692706336015843341e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 3.203396426255936659219646589984 y[1] (numeric) = 3.2033964262559366592196465899848 absolute error = 8e-31 relative error = 2.4973493553372768697378322135591e-29 % Correct digits = 31 bytes used=108042032, alloc=4390108, time=4.09 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 3.2255409284924676045795375313951 y[1] (numeric) = 3.2255409284924676045795375313959 absolute error = 8e-31 relative error = 2.4802041509791004589290075044125e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 3.2479079866764714191794502001334 y[1] (numeric) = 3.2479079866764714191794502001342 absolute error = 8e-31 relative error = 2.4631239655856947159787333460509e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 3.2704998375324057806850092252533 y[1] (numeric) = 3.2704998375324057806850092252541 absolute error = 8e-31 relative error = 2.4461092791357559329549303733660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 3.2933187402641828876675637932731 y[1] (numeric) = 3.2933187402641828876675637932739 absolute error = 8e-31 relative error = 2.4291605614093269782562023047042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 3.3163669767810917335002471928655 y[1] (numeric) = 3.3163669767810917335002471928663 absolute error = 8e-31 relative error = 2.4122782719796897962037851755259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 3.3396468519259909368547269375638 y[1] (numeric) = 3.3396468519259909368547269375646 absolute error = 8e-31 relative error = 2.3954628602082163991880978397113e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 3.3631606937057949482718564674462 y[1] (numeric) = 3.363160693705794948271856467447 absolute error = 8e-31 relative error = 2.3787147652421481055030922595667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 3.3869108535242766816189579740184 y[1] (numeric) = 3.3869108535242766816189579740192 absolute error = 8e-31 relative error = 2.3620344160152716114319706062681e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 3.4108997064172098508908849161329 y[1] (numeric) = 3.4108997064172098508908849161337 absolute error = 8e-31 relative error = 2.3454222312514593592754005299536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 3.4351296512898745267844969337052 y[1] (numeric) = 3.435129651289874526784496933706 absolute error = 8e-31 relative error = 2.3288786194710405741952880971134e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 3.4596031111569496638001265636025 y[1] (numeric) = 3.4596031111569496638001265636032 absolute error = 7e-31 relative error = 2.0233534816249722557583123423977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 3.4843225333848165873226590099968 y[1] (numeric) = 3.4843225333848165873226590099975 absolute error = 7e-31 relative error = 2.0089988607340283542221724944078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 3.5092903899362976712328533227943 y[1] (numeric) = 3.509290389936297671232853322795 absolute error = 7e-31 relative error = 1.9947052600930717991314493875672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 3.5345091776178546801206156940979 y[1] (numeric) = 3.5345091776178546801206156940987 absolute error = 8e-31 relative error = 2.2633977160562197991883590368794e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 3.5599814183292714961404455052082 y[1] (numeric) = 3.559981418329271496140445505209 absolute error = 8e-31 relative error = 2.2472027406689290172719188551525e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 3.5857096593158461989898093013769 y[1] (numeric) = 3.5857096593158461989898093013777 absolute error = 8e-31 relative error = 2.2310785758170952658776250881115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 3.6116964734231177184286012988948 y[1] (numeric) = 3.6116964734231177184286012988956 absolute error = 8e-31 relative error = 2.2150255590048813714952556068677e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 3.6379444593541525322172152885726 y[1] (numeric) = 3.6379444593541525322172152885734 absolute error = 8e-31 relative error = 2.1990440176814153480403665514739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 3.6644562419294171383574280391061 y[1] (numeric) = 3.664456241929417138357428039107 absolute error = 9e-31 relative error = 2.4560260529298342067866609846145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 3.691234472349262289099879404071 y[1] (numeric) = 3.6912344723492622890998794040719 absolute error = 9e-31 relative error = 2.4382086988562415139187155312927e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 3.7182818284590452353602874713527 y[1] (numeric) = 3.7182818284590452353602874713536 absolute error = 9e-31 relative error = 2.4204727923299560867395668236034e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 3.7456010150169164939897763166604 y[1] (numeric) = 3.7456010150169164939897763166613 absolute error = 9e-31 relative error = 2.4028186568502819387005291602730e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=112044908, alloc=4390108, time=4.25 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 3.7731947639642979167991997771454 y[1] (numeric) = 3.7731947639642979167991997771464 absolute error = 1.0e-30 relative error = 2.6502740053348118933845158669641e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 3.8010658346990791093697628196836 y[1] (numeric) = 3.8010658346990791093697628196845 absolute error = 9e-31 relative error = 2.3677569374992179072394802346049e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 3.8292170143515595195194860071813 y[1] (numeric) = 3.8292170143515595195194860071823 absolute error = 1.0e-30 relative error = 2.6114999391575100570062960717259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 3.8576511180631637898643122162488 y[1] (numeric) = 3.8576511180631637898643122162497 absolute error = 9e-31 relative error = 2.3330259073606140558819393564214e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 3.8863709892679582462413752849215 y[1] (numeric) = 3.8863709892679582462413752849225 absolute error = 1.0e-30 relative error = 2.5730945469731423259602329086400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 3.9153794999769966738778707729755 y[1] (numeric) = 3.9153794999769966738778707729765 absolute error = 1.0e-30 relative error = 2.5540308417252404790846409451920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 3.9446795510655238161201013252344 y[1] (numeric) = 3.9446795510655238161201013252354 absolute error = 1.0e-30 relative error = 2.5350601666233783216092668440930e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 3.9742740725630653163119065891359 y[1] (numeric) = 3.9742740725630653163119065891369 absolute error = 1.0e-30 relative error = 2.5161827839293577397920941555007e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 4.0041660239464331120584079535887 y[1] (numeric) = 4.0041660239464331120584079535897 absolute error = 1.0e-30 relative error = 2.4973989440488239579002315758794e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 4.0343583944356755826586664593838 y[1] (numeric) = 4.0343583944356755826586664593848 absolute error = 1.0e-30 relative error = 2.4787088856042984122701949176428e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 4.0648542032930020449686230918988 y[1] (numeric) = 4.0648542032930020449686230918999 absolute error = 1.1e-30 relative error = 2.7061241190615711978036831856143e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 4.0956565001247114903930123270235 y[1] (numeric) = 4.0956565001247114903930123270246 absolute error = 1.1e-30 relative error = 2.6857721099572323404834482998643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 4.1267683651861557561315562411795 y[1] (numeric) = 4.1267683651861557561315562411806 absolute error = 1.1e-30 relative error = 2.6655239709592465507085210727036e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 4.1581929096897676272507006280068 y[1] (numeric) = 4.1581929096897676272507006280079 absolute error = 1.1e-30 relative error = 2.6453799135597781795570870848201e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 4.1899332761161846726477912360218 y[1] (numeric) = 4.1899332761161846726477912360229 absolute error = 1.1e-30 relative error = 2.6253401367279853827498401272717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 4.2219926385284999275505572724101 y[1] (numeric) = 4.2219926385284999275505572724112 absolute error = 1.1e-30 relative error = 2.6054048270045902760496954318382e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 4.2543742028896708478820285629729 y[1] (numeric) = 4.254374202889670847882028562974 absolute error = 1.1e-30 relative error = 2.5855741585985881845702606715037e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 4.2870812073831182776508312036078 y[1] (numeric) = 4.287081207383118277650831203609 absolute error = 1.2e-30 relative error = 2.7991072292574864816100231764912e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 4.3201169227365474895307674296016 y[1] (numeric) = 4.3201169227365474895307674296028 absolute error = 1.2e-30 relative error = 2.7777025980117882848290481704386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 4.3534846525490236810035894273757 y[1] (numeric) = 4.3534846525490236810035894273769 absolute error = 1.2e-30 relative error = 2.7564126114407774422313658158449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 4.3871877336213346338871451880633 y[1] (numeric) = 4.3871877336213346338871451880645 absolute error = 1.2e-30 relative error = 2.7352374068785951055180577864809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 4.4212295362896735737901523514522 y[1] (numeric) = 4.4212295362896735737901523514534 absolute error = 1.2e-30 relative error = 2.7141771087665543490579289285875e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 bytes used=116045972, alloc=4390108, time=4.40 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 4.455613464762675598057615494122 y[1] (numeric) = 4.4556134647626755980576154941232 absolute error = 1.2e-30 relative error = 2.6932318287711184195048436929841e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 4.4903429574618413761305460296723 y[1] (numeric) = 4.4903429574618413761305460296735 absolute error = 1.2e-30 relative error = 2.6724016659037062360057654280615e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 4.5254214873653821649737080556228 y[1] (numeric) = 4.525421487365382164973708055624 absolute error = 1.2e-30 relative error = 2.6516867066422538003685072937690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 4.5608525623555205243594713895519 y[1] (numeric) = 4.5608525623555205243594713895532 absolute error = 1.3e-30 relative error = 2.8503442771423322559018823191229e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 4.5966397255692814623687184072408 y[1] (numeric) = 4.5966397255692814623687184072421 absolute error = 1.3e-30 relative error = 2.8281529064995375458940502300148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 4.6327865557528090905156817025115 y[1] (numeric) = 4.6327865557528090905156817025128 absolute error = 1.3e-30 relative error = 2.8060865406926895520212113299037e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 4.6692966676192442204574899160115 y[1] (numeric) = 4.6692966676192442204574899160128 absolute error = 1.3e-30 relative error = 2.7841452204467380361728498606404e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 4.7061737122101986903463250122245 y[1] (numeric) = 4.7061737122101986903463250122259 absolute error = 1.4e-30 relative error = 2.9748158177155483654392270797923e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 4.7434213772608625685580558298259 y[1] (numeric) = 4.7434213772608625685580558298272 absolute error = 1.3e-30 relative error = 2.7406378152107126577206879094388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 4.7810433875687807458219777860331 y[1] (numeric) = 4.7810433875687807458219777860344 absolute error = 1.3e-30 relative error = 2.7190717477698230190438578003670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 4.8190435053663357937181865600786 y[1] (numeric) = 4.8190435053663357937181865600799 absolute error = 1.3e-30 relative error = 2.6976307612752629204391527297397e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 4.8574255306969743381388389099302 y[1] (numeric) = 4.8574255306969743381388389099315 absolute error = 1.3e-30 relative error = 2.6763148334123152764693635241454e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 4.8961933017952145706641697713002 y[1] (numeric) = 4.8961933017952145706641697713015 absolute error = 1.3e-30 relative error = 2.6551239296931930433579228102745e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 4.9353506954704728989210772223787 y[1] (numeric) = 4.93535069547047289892107722238 absolute error = 1.3e-30 relative error = 2.6340580036046956324990869913907e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 4.9749016274947481189091677809396 y[1] (numeric) = 4.9749016274947481189091677809409 absolute error = 1.3e-30 relative error = 2.6131169967568818585133721309813e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 5.0148500529942018780345658588566 y[1] (numeric) = 5.014850052994201878034565858858 absolute error = 1.4e-30 relative error = 2.7917085958813585820550696751392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 5.0551999668446745872241088952286 y[1] (numeric) = 5.05519996684467458722410889523 absolute error = 1.4e-30 relative error = 2.7694255601798555258391897182732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 5.0959554040711763340407372797126 y[1] (numeric) = 5.095955404071176334040737279714 absolute error = 1.4e-30 relative error = 2.7472767891209078778577093904835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 5.1371204402513927462243008090194 y[1] (numeric) = 5.1371204402513927462243008090208 absolute error = 1.4e-30 relative error = 2.7252621702820907307424521094143e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 5.1786991919232461565803917643529 y[1] (numeric) = 5.1786991919232461565803917643543 absolute error = 1.4e-30 relative error = 2.7033815792650300215464535026078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 5.2206958169965528256733289292909 y[1] (numeric) = 5.2206958169965528256733289292922 absolute error = 1.3e-30 relative error = 2.4900895312990773644806294561149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 5.2631145151688173883886106755809 y[1] (numeric) = 5.2631145151688173883886106755822 absolute error = 1.3e-30 relative error = 2.4700203581990686770877020451460e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=120047580, alloc=4390108, time=4.55 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 5.3059595283452061041559898892827 y[1] (numeric) = 5.305959528345206104155989889284 absolute error = 1.3e-30 relative error = 2.4500752277796528032109570440386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 5.3492351410627409085081719198621 y[1] (numeric) = 5.3492351410627409085081719198635 absolute error = 1.4e-30 relative error = 2.6171965955526490675633083404731e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 5.3929456809187566857337876433172 y[1] (numeric) = 5.3929456809187566857337876433186 absolute error = 1.4e-30 relative error = 2.5959838701017516021572357463792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 5.4370955190036646087089558540139 y[1] (numeric) = 5.4370955190036646087089558540152 absolute error = 1.3e-30 relative error = 2.3909824564535552690309687458675e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 5.4816890703380648226020554601193 y[1] (numeric) = 5.4816890703380648226020554601206 absolute error = 1.3e-30 relative error = 2.3715318094826324251061766774688e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 5.5267307943142521840843397438116 y[1] (numeric) = 5.5267307943142521840843397438129 absolute error = 1.3e-30 relative error = 2.3522043109778461660788126959587e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 5.5722251951421592069882364234397 y[1] (numeric) = 5.572225195142159206988236423441 absolute error = 1.3e-30 relative error = 2.3329997522952484703572637050946e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 5.6181768222997808090795197077546 y[1] (numeric) = 5.6181768222997808090795197077559 absolute error = 1.3e-30 relative error = 2.3139179152212044448948089446887e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 5.6645902709881259027933867662438 y[1] (numeric) = 5.6645902709881259027933867662451 absolute error = 1.3e-30 relative error = 2.2949585721285172473810867656637e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 5.7114701825907413254726398125845 y[1] (numeric) = 5.7114701825907413254726398125859 absolute error = 1.4e-30 relative error = 2.4512077542965574537281264288757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 5.758821245137854061883935504415 y[1] (numeric) = 5.7588212451378540618839355044164 absolute error = 1.4e-30 relative error = 2.4310530582660704658254518293276e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 5.8066481937751781736211397590791 y[1] (numeric) = 5.8066481937751781736211397590805 absolute error = 1.4e-30 relative error = 2.4110294842742890739882539482373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 5.8549558112374333164794020642401 y[1] (numeric) = 5.8549558112374333164794020642415 absolute error = 1.4e-30 relative error = 2.3911367483132426448456783236173e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 5.9037489283266221980462867706038 y[1] (numeric) = 5.9037489283266221980462867706051 absolute error = 1.3e-30 relative error = 2.2019906601422432594523346365093e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 5.953032424395114803654286356424 y[1] (numeric) = 5.9530324243951148036542863564253 absolute error = 1.3e-30 relative error = 2.1837609932589817360485097333984e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 6.0028112278335876995198834453142 y[1] (numeric) = 6.0028112278335876995198834453156 absolute error = 1.4e-30 relative error = 2.3322405900564350583413674864699e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 6.053090316563867207406092924905 y[1] (numeric) = 6.0530903165638672074060929249064 absolute error = 1.4e-30 relative error = 2.3128681826686045893025212740644e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 6.1038747185367257355366544351225 y[1] (numeric) = 6.1038747185367257355366544351239 absolute error = 1.4e-30 relative error = 2.2936250571270248021116406808447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 6.1551695122346810458097983038692 y[1] (numeric) = 6.1551695122346810458097983038706 absolute error = 1.4e-30 relative error = 2.2745108761297450696243490916640e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 6.2069798271798487376573070927123 y[1] (numeric) = 6.2069798271798487376573070927138 absolute error = 1.5e-30 relative error = 2.4166342436487785578717889517530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -12.5 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 6.2593108444468987342204704726538 y[1] (numeric) = 6.2593108444468987342204704726553 absolute error = 1.5e-30 relative error = 2.3964299541550358074595878646936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 6.3121677971811670669190161888314 y[1] (numeric) = 6.3121677971811670669190161888329 absolute error = 1.5e-30 relative error = 2.3763626826743372365460717351472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=124050504, alloc=4390108, time=4.71 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 6.3655559711219747700232352669232 y[1] (numeric) = 6.3655559711219747700232352669247 absolute error = 1.5e-30 relative error = 2.3564320332817908930244278396206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 6.4194807051312062175548592062532 y[1] (numeric) = 6.4194807051312062175548592062547 absolute error = 1.5e-30 relative error = 2.3366376018562109874686490693819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 6.4739473917271997607908626630091 y[1] (numeric) = 6.4739473917271997607908626630106 absolute error = 1.5e-30 relative error = 2.3169789762530205650093064808711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 6.528961477624004055878852351461 y[1] (numeric) = 6.5289614776240040558788523514625 absolute error = 1.5e-30 relative error = 2.2974557364762926295692489673121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 6.5845284642760540076461854730193 y[1] (numeric) = 6.5845284642760540076461854730208 absolute error = 1.5e-30 relative error = 2.2780674548498892098342886598898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 6.640653908428320797651096717808 y[1] (numeric) = 6.6406539084283207976510967178095 absolute error = 1.5e-30 relative error = 2.2588136961876591018246572063660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 6.6973434226719910119370988363601 y[1] (numeric) = 6.6973434226719910119370988363616 absolute error = 1.5e-30 relative error = 2.2396940179626562608782118088272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 6.7546026760057304368664997048427 y[1] (numeric) = 6.7546026760057304368664997048442 absolute error = 1.5e-30 relative error = 2.2207079704753420455927729777648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 6.8124373944025886498803406244497 y[1] (numeric) = 6.8124373944025886498803406244512 absolute error = 1.5e-30 relative error = 2.2018550970207357371654805967865e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 6.8708533613826010961162539158285 y[1] (numeric) = 6.87085336138260109611625391583 absolute error = 1.5e-30 relative error = 2.1831349340544789690005248007338e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 6.9298564185911459115690715820469 y[1] (numeric) = 6.9298564185911459115690715820484 absolute error = 1.5e-30 relative error = 2.1645470113577809028476749991272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 6.9894524663831133289584667268155 y[1] (numeric) = 6.989452466383113328958466726817 absolute error = 1.5e-30 relative error = 2.1460908522012121785228664007476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 7.0496474644129460837310239530277 y[1] (numeric) = 7.0496474644129460837310239530292 absolute error = 1.5e-30 relative error = 2.1277659735073168439141716270643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 7.1104474322306098247290409259947 y[1] (numeric) = 7.1104474322306098247290409259962 absolute error = 1.5e-30 relative error = 2.1095718860120126399822679206578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 7.1718584498835531270637716458996 y[1] (numeric) = 7.1718584498835531270637716459011 absolute error = 1.5e-30 relative error = 2.0915080944247511713392185109442e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 7.2338866585247173036960337699729 y[1] (numeric) = 7.2338866585247173036960337699744 absolute error = 1.5e-30 relative error = 2.0735740975874106362726477608739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 7.2965382610266568172120145770248 y[1] (numeric) = 7.2965382610266568172120145770263 absolute error = 1.5e-30 relative error = 2.0557693886318949203379205879770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 7.3598195226018317043472218706367 y[1] (numeric) = 7.3598195226018317043472218706382 absolute error = 1.5e-30 relative error = 2.0380934551364139744561977865411e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 7.4237367714291340430179442929097 y[1] (numeric) = 7.4237367714291340430179442929112 absolute error = 1.5e-30 relative error = 2.0205457792804215014420733998626e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 7.4882963992867111150290313243491 y[1] (numeric) = 7.4882963992867111150290313243506 absolute error = 1.5e-30 relative error = 2.0031258379981870636747583985531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 7.5535048621911485473016181413198 y[1] (numeric) = 7.5535048621911485473016181413213 absolute error = 1.5e-30 relative error = 1.9858331031309807988779247283513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 7.6193686810430773504675724967601 y[1] (numeric) = 7.6193686810430773504675724967615 absolute error = 1.4e-30 relative error = 1.8374225721393266576731130248276e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=128051608, alloc=4390108, time=4.86 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 7.6858944422792694160725307276929 y[1] (numeric) = 7.6858944422792694160725307276943 absolute error = 1.4e-30 relative error = 1.8215186410819699301745638750378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -6.667e+29 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 7.7530887985312866824806579188518 y[1] (numeric) = 7.7530887985312866824806579188532 absolute error = 1.4e-30 relative error = 1.8057319300472996689436052947328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 7.8209584692907498349465988329418 y[1] (numeric) = 7.8209584692907498349465988329432 absolute error = 1.4e-30 relative error = 1.7900619284671385958940052576832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 7.8895102415812930672790192339938 y[1] (numeric) = 7.8895102415812930672790192339953 absolute error = 1.5e-30 relative error = 1.9012587018321117985758484380057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 7.958750970637272101131868125876 y[1] (numeric) = 7.9587509706372721011318681258775 absolute error = 1.5e-30 relative error = 1.8847178477301849660884982728838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 8.0286875805892933342908819335644 y[1] (numeric) = 8.0286875805892933342908819335659 absolute error = 1.5e-30 relative error = 1.8683003728112463237545933847705e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -6.667e+29 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 8.099327065156632671441435472082 y[1] (numeric) = 8.0993270651566326714414354720835 absolute error = 1.5e-30 relative error = 1.8520057134783598713176651764499e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 8.1706764883466132798778341038975 y[1] (numeric) = 8.1706764883466132798778341038991 absolute error = 1.6e-30 relative error = 1.9582221891687818572070548016264e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 8.2427429851610122085124347531447 y[1] (numeric) = 8.2427429851610122085124347531463 absolute error = 1.6e-30 relative error = 1.9411014062677897478602786149431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 8.315533762309566511435170833514 y[1] (numeric) = 8.3155337623095665114351708335156 absolute error = 1.6e-30 relative error = 1.9241097994840129712596443233579e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 8.389056098930650227230427460575 y[1] (numeric) = 8.3890560989306502272304274605766 absolute error = 1.6e-30 relative error = 1.9072467523538808950443337391617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 8.4633173473191942823497647873654 y[1] (numeric) = 8.463317347319194282349764787367 absolute error = 1.6e-30 relative error = 1.8905116449483126645442153958760e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.325e+15 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 8.5383249336619221111374286770603 y[1] (numeric) = 8.538324933661922111137428677062 absolute error = 1.7e-30 relative error = 1.9910228448882689008327422779350e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 8.6140863587799745166833496561362 y[1] (numeric) = 8.6140863587799745166833496561379 absolute error = 1.7e-30 relative error = 1.9735116751729123058540922957532e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 8.6906091988789980356085715614843 y[1] (numeric) = 8.690609198878998035608571561486 absolute error = 1.7e-30 relative error = 1.9561344447743468381026475098633e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 8.7679011063067718162446641452442 y[1] (numeric) = 8.7679011063067718162446641452459 absolute error = 1.7e-30 relative error = 1.9388904817564445560264606902608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 8.8459698103184487735262954149556 y[1] (numeric) = 8.8459698103184487735262954149572 absolute error = 1.6e-30 relative error = 1.8087332811532635227228467303004e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 8.9248231178494875453501560543463 y[1] (numeric) = 8.9248231178494875453501560543479 absolute error = 1.6e-30 relative error = 1.7927526169118449521467964985130e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 9.0044689142963525442399839278696 y[1] (numeric) = 9.0044689142963525442399839278712 absolute error = 1.6e-30 relative error = 1.7768954673825211350374477495610e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 9.0849151643050601749734407164419 y[1] (numeric) = 9.0849151643050601749734407164435 absolute error = 1.6e-30 relative error = 1.7611611898000481822972765699160e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 9.1661699125676500734497274104786 y[1] (numeric) = 9.1661699125676500734497274104803 absolute error = 1.7e-30 relative error = 1.8546459603254199510848032309440e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 9.2482412846266610145855536665902 y[1] (numeric) = 9.2482412846266610145855536665919 absolute error = 1.7e-30 relative error = 1.8381873349540606189572868625910e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=132054448, alloc=4390108, time=5.02 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 9.3311374876876919375006494494469 y[1] (numeric) = 9.3311374876876919375006494494486 absolute error = 1.7e-30 relative error = 1.8218571982709789745349109134641e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 9.414866811440129344772473954749 y[1] (numeric) = 9.4148668114401293447724739547508 absolute error = 1.8e-30 relative error = 1.9118698501531600663619671142209e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 9.4994376288861231491839890633767 y[1] (numeric) = 9.4994376288861231491839890633785 absolute error = 1.8e-30 relative error = 1.8948490114051760398363528260256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 9.5848583971778938662399876124018 y[1] (numeric) = 9.5848583971778938662399876124036 absolute error = 1.8e-30 relative error = 1.8779620161420233526582639445433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 9.6711376584634548838689864354103 y[1] (numeric) = 9.6711376584634548838689864354121 absolute error = 1.8e-30 relative error = 1.8612081262484924918844011214117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 9.7582840407408343822424252687577 y[1] (numeric) = 9.7582840407408343822424252687596 absolute error = 1.9e-30 relative error = 1.9470636354378498204130682184750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 9.8463062587208823266150074163392 y[1] (numeric) = 9.8463062587208823266150074163411 absolute error = 1.9e-30 relative error = 1.9296576300550963339815588430711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 9.9352131146987488146044744309985 y[1] (numeric) = 9.9352131146987488146044744310004 absolute error = 1.9e-30 relative error = 1.9123897777180303280767462719076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 10.025013499434120926471777166889 y[1] (numeric) = 10.025013499434120926471777166891 absolute error = 2e-30 relative error = 1.9950097823937029398853866939930e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 10.115716393040306102820204373562 y[1] (numeric) = 10.115716393040306102820204373564 absolute error = 2e-30 relative error = 1.9771214635633873824245698337483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 10.20733086588225095879214402908 y[1] (numeric) = 10.207330865882250958792144029082 absolute error = 2e-30 relative error = 1.9593760859510787073458172262453e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 10.299866079483585337393248594605 y[1] (numeric) = 10.299866079483585337393248594607 absolute error = 2e-30 relative error = 1.9417728197299784654636807809679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 10.393331287442782307105209171014 y[1] (numeric) = 10.393331287442782307105209171016 absolute error = 2e-30 relative error = 1.9243108342138569232387866587707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 10.487735836358525720550369044512 y[1] (numeric) = 10.487735836358525720550369044514 absolute error = 2e-30 relative error = 1.9069892979821898793922952645667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 10.583089166764377871735185285297 y[1] (numeric) = 10.583089166764377871735185285299 absolute error = 2e-30 relative error = 1.8898073790031859453434842247641e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 10.679400814072840719417155056108 y[1] (numeric) = 10.67940081407284071941715505611 absolute error = 2e-30 relative error = 1.8727642447547138673311472163336e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 10.776680409528905083504263631818 y[1] (numeric) = 10.77668040952890508350426363182 absolute error = 2e-30 relative error = 1.8558590623431400217242219529765e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 10.874937681173183170201221053971 y[1] (numeric) = 10.874937681173183170201221053973 absolute error = 2e-30 relative error = 1.8390909986200867490350857047855e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 10.974182454814720739957615156909 y[1] (numeric) = 10.974182454814720739957615156911 absolute error = 2e-30 relative error = 1.8224592202971227067860949395282e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 11.074424655013586200245455289684 y[1] (numeric) = 11.074424655013586200245455289687 absolute error = 3e-30 relative error = 2.7089443410875953753760213734310e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 11.175674306073334882894211461532 y[1] (numeric) = 11.175674306073334882894211461535 absolute error = 3e-30 relative error = 2.6844017800068429902060699308180e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 11.277941533043447753238138736105 y[1] (numeric) = 11.277941533043447753238138736107 absolute error = 2e-30 relative error = 1.7733732650946658277891477139213e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=136055748, alloc=4390108, time=5.18 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 11.381236562731844795782169982426 y[1] (numeric) = 11.381236562731844795782169982428 absolute error = 2e-30 relative error = 1.7572782965860247817158552757443e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 11.485569724727574328568707539109 y[1] (numeric) = 11.485569724727574328568707539111 absolute error = 2e-30 relative error = 1.7413154488054251945533768750134e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 11.590951452433780516028994407103 y[1] (numeric) = 11.590951452433780516028994407106 absolute error = 3e-30 relative error = 2.5882258348775006207098090872434e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 11.69739228411105237793115923818 y[1] (numeric) = 11.697392284111052377931159238183 absolute error = 3e-30 relative error = 2.5646741830441964199201416500130e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 11.804902863931258630195290329287 y[1] (numeric) = 11.80490286393125863019529032929 absolute error = 3e-30 relative error = 2.5413169719220735478436275797763e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 11.913493943041973741937818758192 y[1] (numeric) = 11.913493943041973741937818758195 absolute error = 3e-30 relative error = 2.5181529569267439294005944512303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 12.023176380641601652237939769668 y[1] (numeric) = 12.02317638064160165223793976967 absolute error = 2e-30 relative error = 1.6634539298784474132590487818768e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 12.133961145065304659893688471457 y[1] (numeric) = 12.133961145065304659893688471459 absolute error = 2e-30 relative error = 1.6482663625582559524323354079179e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 12.245859314881846079961589205531 y[1] (numeric) = 12.245859314881846079961589205532 absolute error = 1e-30 relative error = 8.1660255461594650803329554070764e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 12.358882080001456352259571153473 y[1] (numeric) = 12.358882080001456352259571153475 absolute error = 2e-30 relative error = 1.6182693443093069166805919077044e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 12.473040742794833389367225302064 y[1] (numeric) = 12.473040742794833389367225302065 absolute error = 1e-30 relative error = 8.0172912172812326446118707227730e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 12.58834671922338906509070619308 y[1] (numeric) = 12.588346719223389065090706193082 absolute error = 2e-30 relative error = 1.5887709836795674880324671641767e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 12.704811539980854868983000160809 y[1] (numeric) = 12.704811539980854868983000160811 absolute error = 2e-30 relative error = 1.5742067434107045710927910849835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 12.822446851646360888436353300643 y[1] (numeric) = 12.822446851646360888436353300645 absolute error = 2e-30 relative error = 1.5597647025873275036033128979139e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 12.941264417849103427205970766319 y[1] (numeric) = 12.941264417849103427205970766321 absolute error = 2e-30 relative error = 1.5454440427331976495508299090890e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 13.061276120444717728097399349678 y[1] (numeric) = 13.061276120444717728097399349681 absolute error = 3e-30 relative error = 2.2968659205543648675323097838826e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 13.182493960703473438070175951168 y[1] (numeric) = 13.182493960703473438070175951171 absolute error = 3e-30 relative error = 2.2757454006373065357991852993874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 13.304930060510411636294418494051 y[1] (numeric) = 13.304930060510411636294418494054 absolute error = 3e-30 relative error = 2.2548032844637983888849396547795e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 13.428596663577543439863282465196 y[1] (numeric) = 13.428596663577543439863282465199 absolute error = 3e-30 relative error = 2.2340383549808421112214214940815e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 13.553506136668231408032023200075 y[1] (numeric) = 13.553506136668231408032023200079 absolute error = 4e-30 relative error = 2.9512658640986113806084854742601e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 13.679670970833876184144409056144 y[1] (numeric) = 13.679670970833876184144409056148 absolute error = 4e-30 relative error = 2.9240469368951281799727923461024e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 13.807103782663032044941253752753 y[1] (numeric) = 13.807103782663032044941253752757 absolute error = 4e-30 relative error = 2.8970594144607087137569402459077e-29 % Correct digits = 31 h = 0.01 bytes used=140056932, alloc=4390108, time=5.32 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 13.935817315543076269846931825039 y[1] (numeric) = 13.935817315543076269846931825043 absolute error = 4e-30 relative error = 2.8703016905500534874484851515217e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 14.065824440934558498222200489047 y[1] (numeric) = 14.065824440934558498222200489051 absolute error = 4e-30 relative error = 2.8437721633714865673180153336380e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 14.197138159658357510581014537849 y[1] (numeric) = 14.197138159658357510581014537853 absolute error = 4e-30 relative error = 2.8174692357126830414356048904553e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 14.329771603195774150522090176603 y[1] (numeric) = 14.329771603195774150522090176606 absolute error = 3e-30 relative error = 2.0935434862974025240916514896076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 14.463738035001690397750825332584 y[1] (numeric) = 14.463738035001690397750825332588 absolute error = 4e-30 relative error = 2.7655368137338727141009256812650e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 14.599050851830925909193181507426 y[1] (numeric) = 14.59905085183092590919318150743 absolute error = 4e-30 relative error = 2.7399041489730435800858492079938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 14.735723585077924664960939361653 y[1] (numeric) = 14.735723585077924664960939361657 absolute error = 4e-30 relative error = 2.7144917430797799632030266437959e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 14.873769902129905688949333816751 y[1] (numeric) = 14.873769902129905688949333816756 absolute error = 5e-30 relative error = 3.3616225293925019675439957511022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 15.013203607733613160266757797534 y[1] (numeric) = 15.013203607733613160266757797539 absolute error = 5e-30 relative error = 3.3304017787545331747081697597851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.000e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 15.154038645375802591646639807897 y[1] (numeric) = 15.154038645375802591646639807902 absolute error = 5e-30 relative error = 3.2994504745609389305243033806108e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 15.2962890986776011246097455111 y[1] (numeric) = 15.296289098677601124609745511106 absolute error = 6e-30 relative error = 3.9225200055343577445861957130013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 15.439969192802881378568390330594 y[1] (numeric) = 15.439969192802881378568390330599 absolute error = 5e-30 relative error = 3.2383484303392766995078352991235e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 15.585093295880789692431122279052 y[1] (numeric) = 15.585093295880789692431122279057 absolute error = 5e-30 relative error = 3.2081938202586971393420147604504e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 15.731675920442571012717479636724 y[1] (numeric) = 15.731675920442571012717479636729 absolute error = 5e-30 relative error = 3.1783009167527636270142434678787e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 15.879731724872834111868993019468 y[1] (numeric) = 15.879731724872834111868993019474 absolute error = 6e-30 relative error = 3.7784013634197893708493797105364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 16.029275514875402264487654649923 y[1] (numeric) = 16.029275514875402264487654649929 absolute error = 6e-30 relative error = 3.7431510827996637718655758982158e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 16.18032224495389596779102498073 y[1] (numeric) = 16.180322244953895967791024980736 absolute error = 6e-30 relative error = 3.7082079758153150020872509107528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 16.332887019907195765789845226944 y[1] (numeric) = 16.332887019907195765789845226951 absolute error = 7e-30 relative error = 4.2858313973935603272659475536726e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 16.486985096339934724716796743092 y[1] (numeric) = 16.486985096339934724716796743099 absolute error = 7e-30 relative error = 4.2457732320956490203609280428981e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 16.642631884188171610212698046157 y[1] (numeric) = 16.642631884188171610212698046163 absolute error = 6e-30 relative error = 3.6051990104404573211834067356944e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472e+15 Order of pole (six term test) = -10.75 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 16.799842948260397334859256656509 y[1] (numeric) = 16.799842948260397334859256656516 absolute error = 7e-30 relative error = 4.1667056183551056468981723891514e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 16.958634009794028777987305352163 y[1] (numeric) = 16.95863400979402877798730535217 absolute error = 7e-30 relative error = 4.1276909425354233201902063161774e-29 % Correct digits = 31 h = 0.01 bytes used=144057816, alloc=4390108, time=5.48 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 17.119020948027545628439586166743 y[1] (numeric) = 17.11902094802754562843958616675 absolute error = 7e-30 relative error = 4.0890188879677376164999124040392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 17.281019801788427465282476812269 y[1] (numeric) = 17.281019801788427465282476812275 absolute error = 6e-30 relative error = 3.4720173165816608155896559703238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 17.444646771097049871498016010925 y[1] (numeric) = 17.444646771097049871498016010931 absolute error = 6e-30 relative error = 3.4394505539321247724974704392328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 17.609918218786699971604181488378 y[1] (numeric) = 17.609918218786699971604181488384 absolute error = 6e-30 relative error = 3.4071708485273090886203779979901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 17.776850672139873396107200104494 y[1] (numeric) = 17.7768506721398733961072001045 absolute error = 6e-30 relative error = 3.3751760143900421614796416799682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 17.945460824541016303845920701474 y[1] (numeric) = 17.945460824541016303845920701481 absolute error = 7e-30 relative error = 3.9007078550065799889487190428670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 18.11576553714587773780777371626 y[1] (numeric) = 18.115765537145877737807773716266 absolute error = 6e-30 relative error = 3.3120322669760576414633456991519e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 18.287781840567639251043030753446 y[1] (numeric) = 18.287781840567639251043030753452 absolute error = 6e-30 relative error = 3.2808790329564454320376899412194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 18.46152693657999041704506824997 y[1] (numeric) = 18.461526936579990417045068249976 absolute error = 6e-30 relative error = 3.2500020288741640827339177807047e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 18.637018199837320533566907580682 y[1] (numeric) = 18.637018199837320533566907580688 absolute error = 6e-30 relative error = 3.2193991204303127273410491340570e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 18.814273179612198540477911123657 y[1] (numeric) = 18.814273179612198540477911123663 absolute error = 6e-30 relative error = 3.1890681838838233184528260365198e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 18.993309601550314901100324712728 y[1] (numeric) = 18.993309601550314901100324712734 absolute error = 6e-30 relative error = 3.1590071061181745918943573258470e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 19.174145369443060942676256574128 y[1] (numeric) = 19.174145369443060942676256574134 absolute error = 6e-30 relative error = 3.1292137847050640867973194993343e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 19.356798567017922915376293819354 y[1] (numeric) = 19.35679856701792291537629381936 absolute error = 6e-30 relative error = 3.0996861279650906121781625618598e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 19.541287459746869810747657378403 y[1] (numeric) = 19.54128745974686981074765737841 absolute error = 7e-30 relative error = 3.5821590641964156747455181871680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 19.727630496672915779890735060899 y[1] (numeric) = 19.727630496672915779890735060905 absolute error = 6e-30 relative error = 3.0414194958750397728433995373188e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 19.915846312255039809127950820668 y[1] (numeric) = 19.915846312255039809127950820674 absolute error = 6e-30 relative error = 3.0126763914159917417708270277570e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 20.105953728231647146669975298563 y[1] (numeric) = 20.10595372823164714666997529857 absolute error = 7e-30 relative error = 3.4815558090989707628780008997033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 20.297971755502758827974833963076 y[1] (numeric) = 20.297971755502758827974833963083 absolute error = 7e-30 relative error = 3.4486204258818654384591028599882e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 20.491919596031117520320945259013 y[1] (numeric) = 20.49191959603111752032094525902 absolute error = 7e-30 relative error = 3.4159806099159995529954637395678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 20.687816644762399798762806219384 y[1] (numeric) = 20.687816644762399798762806219391 absolute error = 7e-30 relative error = 3.3836340103933646460342783298150e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 20.885682491564726876297103339624 y[1] (numeric) = 20.885682491564726876297103339631 absolute error = 7e-30 relative error = 3.3515782894943212062788742536485e-29 % Correct digits = 31 h = 0.01 bytes used=148059968, alloc=4390108, time=5.63 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 21.085536923187667740928529654582 y[1] (numeric) = 21.085536923187667740928529654589 absolute error = 7e-30 relative error = 3.3198111224296746615193706240226e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 21.28739992524093060158152265589 y[1] (numeric) = 21.287399925240930601581522655897 absolute error = 7e-30 relative error = 3.2883301974798474890456821794874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 21.491291684192940513651429258142 y[1] (numeric) = 21.491291684192940513651429258149 absolute error = 7e-30 relative error = 3.2571332160312029314071920074647e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 21.697232589389503043623139836616 y[1] (numeric) = 21.697232589389503043623139836623 absolute error = 7e-30 relative error = 3.2262178926095752474047066288611e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 21.905243235092755840805878527866 y[1] (numeric) = 21.905243235092755840805878527874 absolute error = 8e-30 relative error = 3.6520936627554981350385947079987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 22.115344422540612013040455245769 y[1] (numeric) = 22.115344422540612013040455245776 absolute error = 7e-30 relative error = 3.1652231438301242634154512337858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 22.327557162026901252432758671981 y[1] (numeric) = 22.327557162026901252432758671989 absolute error = 8e-30 relative error = 3.5830162439829391478124453191738e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 22.541902675002416726959520286426 y[1] (numeric) = 22.541902675002416726959520286433 absolute error = 7e-30 relative error = 3.1053279312409459362671309487259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 22.758402396197077844386388260106 y[1] (numeric) = 22.758402396197077844386388260114 absolute error = 8e-30 relative error = 3.5151852316913060557662270198029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 22.977077975763421106543177882497 y[1] (numeric) = 22.977077975763421106543177882505 absolute error = 8e-30 relative error = 3.4817307964217749155595242127412e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 23.197951281441633404827974381257 y[1] (numeric) = 23.197951281441633404827974381265 absolute error = 8e-30 relative error = 3.4485803952868898043016994936912e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 23.421044400746344262073838971462 y[1] (numeric) = 23.421044400746344262073838971469 absolute error = 7e-30 relative error = 2.9887650952819743734591839044445e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 23.646379643175395701824637747618 y[1] (numeric) = 23.646379643175395701824637747625 absolute error = 7e-30 relative error = 2.9602840289423656913898845976937e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 23.873979542440810623847568694562 y[1] (numeric) = 23.87397954244081062384756869457 absolute error = 8e-30 relative error = 3.3509285646234166940947659197587e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 24.103866858722182784579084580015 y[1] (numeric) = 24.103866858722182784579084580023 absolute error = 8e-30 relative error = 3.3189695441356680486142655530596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 24.33606458094271372338008756421 y[1] (numeric) = 24.336064580942713723380087564218 absolute error = 8e-30 relative error = 3.2873022560372008616002533817217e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 24.57059592906812424018972480695 y[1] (numeric) = 24.570595929068124240189724806959 absolute error = 9e-30 relative error = 3.6629148214319839466890068433622e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 24.807484356428670317641316402232 y[1] (numeric) = 24.80748435642867031764131640224 absolute error = 8e-30 relative error = 3.2248332338167376616895489255528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 25.046753552064495691167646951714 y[1] (numeric) = 25.046753552064495691167646951723 absolute error = 9e-30 relative error = 3.5932800557532410745399294111043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 25.288427443094555604307098296172 y[1] (numeric) = 25.288427443094555604307098296181 absolute error = 9e-30 relative error = 3.5589401595857659144249370261236e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 25.532530197109348643560263727964 y[1] (numeric) = 25.532530197109348643560263727973 absolute error = 9e-30 relative error = 3.5249150517087922792531099610029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 25.779086224587695927974479188157 y[1] (numeric) = 25.779086224587695927974479188166 absolute error = 9e-30 relative error = 3.4912021014212437175972878799743e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=152065048, alloc=4390108, time=5.78 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 26.02812018133780933338921927269 y[1] (numeric) = 26.028120181337809333389219272698 absolute error = 8e-30 relative error = 3.0735988401252306951883064335115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 26.279656970962892860199012888142 y[1] (numeric) = 26.279656970962892860199012888151 absolute error = 9e-30 relative error = 3.4247022363892894705570869978231e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 26.533721747351523706825329504055 y[1] (numeric) = 26.533721747351523706825329504064 absolute error = 9e-30 relative error = 3.3919101457745328775697473000280e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 26.790339917193062089080107669377 y[1] (numeric) = 26.790339917193062089080107669386 absolute error = 9e-30 relative error = 3.3594198609716514177942749434649e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 27.049537142518341348499043982636 y[1] (numeric) = 27.049537142518341348499043982645 absolute error = 9e-30 relative error = 3.3272288367009337315639429512170e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 27.311339343265892420772724659149 y[1] (numeric) = 27.311339343265892420772724659158 absolute error = 9e-30 relative error = 3.2953345447040896342412907919181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 27.575772699873959288860970327214 y[1] (numeric) = 27.575772699873959288860970327223 absolute error = 9e-30 relative error = 3.2637344737183507250926980434198e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 27.842863655898564624495725565399 y[1] (numeric) = 27.842863655898564624495725565408 absolute error = 9e-30 relative error = 3.2324261294485535284205265739128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 28.112638920657887426818372110231 y[1] (numeric) = 28.112638920657887426818372110241 absolute error = 1.0e-29 relative error = 3.5571189272636172777356474040628e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 28.385125471903217098118984843308 y[1] (numeric) = 28.385125471903217098118984843318 absolute error = 1.0e-29 relative error = 3.5229719205921487725076433812097e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 28.660350558516751054310906965868 y[1] (numeric) = 28.660350558516751054310906965878 absolute error = 1.0e-29 relative error = 3.4891408531736837377969116147084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 28.938341703236505652149863987642 y[1] (numeric) = 28.938341703236505652149863987652 absolute error = 1.0e-29 relative error = 3.4556230286276513396808558380102e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 29.2191267054086129265611051166 y[1] (numeric) = 29.21912670540861292656110511661 absolute error = 1.0e-29 relative error = 3.4224157692395877742103838228075e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.564e+15 Order of pole (six term test) = -6.458e+29 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 29.502733643767278370041893023457 y[1] (numeric) = 29.502733643767278370041893023468 absolute error = 1.1e-29 relative error = 3.7284680575095963525619921094800e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 29.789190879242677752233921434877 y[1] (numeric) = 29.789190879242677752233921434888 absolute error = 1.1e-29 relative error = 3.6926145609630770595620255687588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 30.078527057797073771687539613154 y[1] (numeric) = 30.078527057797073771687539613164 absolute error = 1.0e-29 relative error = 3.3246308839474108401937615014541e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 30.370771113289436153846398566086 y[1] (numeric) = 30.370771113289436153846398566097 absolute error = 1.1e-29 relative error = 3.6219034277949875839972035830613e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 30.665952270368851659649508823945 y[1] (numeric) = 30.665952270368851659649508823956 absolute error = 1.1e-29 relative error = 3.5870400837442154641389726851017e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 30.96410004739701334816275303373 y[1] (numeric) = 30.964100047397013348162753033742 absolute error = 1.2e-29 relative error = 3.8754557638140611686530745352397e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 31.265244259400081344601532358897 y[1] (numeric) = 31.265244259400081344601532358909 absolute error = 1.2e-29 relative error = 3.8381276987439906989000478635566e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 31.569415021050210302281241122151 y[1] (numeric) = 31.569415021050210302281241122163 absolute error = 1.2e-29 relative error = 3.8011474054867677378416049672895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 31.876642749677041713726379239121 y[1] (numeric) = 31.876642749677041713726379239133 absolute error = 1.2e-29 relative error = 3.7645118697832688262669037909821e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -5.000e+29 bytes used=156066888, alloc=4390108, time=5.94 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 32.186958168309462222678998645337 y[1] (numeric) = 32.186958168309462222678998645349 absolute error = 1.2e-29 relative error = 3.7282180991600888994078568225087e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 32.500392308747932115372491603845 y[1] (numeric) = 32.500392308747932115372491603857 absolute error = 1.2e-29 relative error = 3.6922631228577610999836166311139e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 32.81697651466769122648013054928 y[1] (numeric) = 32.816976514667691226480130549292 absolute error = 1.2e-29 relative error = 3.6566439917572990005261509280186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 33.136742444753152582914967864034 y[1] (numeric) = 33.136742444753152582914967864045 absolute error = 1.1e-29 relative error = 3.3195779634463531602612582487487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.000e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 33.459722075863797227457478986324 y[1] (numeric) = 33.459722075863797227457478986336 absolute error = 1.2e-29 relative error = 3.5864015764363480972435767195133e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 33.785947706231886814331566095013 y[1] (numeric) = 33.785947706231886814331566095025 absolute error = 1.2e-29 relative error = 3.5517725014967023044440827778158e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 34.115451958692313750653249350389 y[1] (numeric) = 34.1154519586923137506532493504 absolute error = 1.1e-29 relative error = 3.2243453826491950751818513925599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 34.448267783944911871457741316409 y[1] (numeric) = 34.44826778394491187145774131642 absolute error = 1.1e-29 relative error = 3.1931939419974844177882543581868e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 34.78442846384955388209100856303 y[1] (numeric) = 34.784428463849553882091008563041 absolute error = 1.1e-29 relative error = 3.1623345519193970608418659919516e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 35.123967614754365080455983293164 y[1] (numeric) = 35.123967614754365080455983293175 absolute error = 1.1e-29 relative error = 3.1317646459106972034722128608836e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 35.466919190857386183259170295692 y[1] (numeric) = 35.466919190857386183259170295703 absolute error = 1.1e-29 relative error = 3.1014816767156829688751008959524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 35.813317487602021425341668911734 y[1] (numeric) = 35.813317487602021425341668911745 absolute error = 1.1e-29 relative error = 3.0714831162480320866020833144505e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 36.163197145106611479734092630969 y[1] (numeric) = 36.16319714510661147973409263098 absolute error = 1.1e-29 relative error = 3.0417664555105450640368842518309e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 36.516593151628474158585378769949 y[1] (numeric) = 36.51659315162847415858537876996 absolute error = 1.1e-29 relative error = 3.0123292045138252370976503618120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.270e+15 Order of pole (six term test) = -3.333e+29 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 36.873540847062759301922291319834 y[1] (numeric) = 36.873540847062759301922291319845 absolute error = 1.1e-29 relative error = 2.9831688921939343690501970508438e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 37.234075926476467742644215040193 y[1] (numeric) = 37.234075926476467742644215040205 absolute error = 1.2e-29 relative error = 3.2228542541771582761379822230451e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 37.598234443677987752594765899184 y[1] (numeric) = 37.598234443677987752594765899196 absolute error = 1.2e-29 relative error = 3.1916392292239026212161011121533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 37.966052814822505926329448641597 y[1] (numeric) = 37.966052814822505926329448641609 absolute error = 1.2e-29 relative error = 3.1607183550340064177293187974797e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 38.337567822053653046672257335396 y[1] (numeric) = 38.337567822053653046672257335409 absolute error = 1.3e-29 relative error = 3.3909297690297820971361853627484e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 38.71281661718174909968248956046 y[1] (numeric) = 38.712816617181749099682489560473 absolute error = 1.3e-29 relative error = 3.3580610082063271597647603128708e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 39.091836725399015266598485317448 y[1] (numeric) = 39.091836725399015266598485317461 absolute error = 1.3e-29 relative error = 3.3255024805609993691373433055222e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 39.474666049032124417053505344034 y[1] (numeric) = 39.474666049032124417053505344047 absolute error = 1.3e-29 relative error = 3.2932514194933248241483596484685e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=160067788, alloc=4390108, time=6.09 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 39.861342871332465361740206261101 y[1] (numeric) = 39.861342871332465361740206261114 absolute error = 1.3e-29 relative error = 3.2613050799523760235751456754522e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 40.251905860304499894107543068851 y[1] (numeric) = 40.251905860304499894107543068865 absolute error = 1.4e-29 relative error = 3.4780961797405167657214917912561e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 40.646394072572595459984576852157 y[1] (numeric) = 40.646394072572595459984576852171 absolute error = 1.4e-29 relative error = 3.4443399763835214574573544217082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 41.044846957286720141620521375166 y[1] (numeric) = 41.044846957286720141620521375181 absolute error = 1.5e-29 relative error = 3.6545391472916771586862757393923e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 41.447304360067390528894189239039 y[1] (numeric) = 41.447304360067390528894189239054 absolute error = 1.5e-29 relative error = 3.6190532126503801920570372205792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 41.853806526990266975767426064963 y[1] (numeric) = 41.853806526990266975767426064978 absolute error = 1.5e-29 relative error = 3.5839034115874141604274871000755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 42.264394108610794704828685161265 y[1] (numeric) = 42.26439410861079470482868516128 absolute error = 1.5e-29 relative error = 3.5490867233191814013457110931118e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 42.679108164029293227391075798772 y[1] (numeric) = 42.679108164029293227391075798787 absolute error = 1.5e-29 relative error = 3.5146001510505472899362566672851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 43.097990164996900591474480707947 y[1] (numeric) = 43.097990164996900591474480707962 absolute error = 1.5e-29 relative error = 3.4804407218466120624872497672857e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.071 Order of pole (six term test) = 1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 43.521082000062783055518172621604 y[1] (numeric) = 43.521082000062783055518172621619 absolute error = 1.5e-29 relative error = 3.4466054865038422430855830035238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 43.948425978763024912247320706349 y[1] (numeric) = 43.948425978763024912247320706365 absolute error = 1.6e-29 relative error = 3.6406309540486384853653736048456e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 44.380064835851617355166526689092 y[1] (numeric) = 44.380064835851617355166526689108 absolute error = 1.6e-29 relative error = 3.6052223130315697320226482904391e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 44.816041735573969490092875840424 y[1] (numeric) = 44.81604173557396949009287584044 absolute error = 1.6e-29 relative error = 3.5701501918451576681804795270083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 45.256400275983368846390927167131 y[1] (numeric) = 45.256400275983368846390927167147 absolute error = 1.6e-29 relative error = 3.5354115445392300686674375872220e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 45.701184493300823037557828729065 y[1] (numeric) = 45.701184493300823037557828729081 absolute error = 1.6e-29 relative error = 3.5010033497808758323602075177078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 46.150438866318718558957830086431 y[1] (numeric) = 46.150438866318718558957830086447 absolute error = 1.6e-29 relative error = 3.4669226107136848093065546069869e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 46.604208320848737092255693225917 y[1] (numeric) = 46.604208320848737092255693225933 absolute error = 1.6e-29 relative error = 3.4331663548165631487500593298207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 47.062538234214474111886054582464 y[1] (numeric) = 47.06253823421447411188605458248 absolute error = 1.6e-29 relative error = 3.3997316337621579880977300155795e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 47.525474439789209059163246411121 y[1] (numeric) = 47.525474439789209059163246411138 absolute error = 1.7e-29 relative error = 3.5770289934796073401794726438903e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 47.993063231579280864830476241162 y[1] (numeric) = 47.993063231579280864830476241179 absolute error = 1.7e-29 relative error = 3.5421785681756722734504968635106e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 48.46535136885352716142011166414 y[1] (numeric) = 48.465351368853527161420111664157 absolute error = 1.7e-29 relative error = 3.5076605285740536976729841226902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 48.942386080819250133204185354246 y[1] (numeric) = 48.942386080819250133204185354263 absolute error = 1.7e-29 relative error = 3.4734718433890127518201001460762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=164071484, alloc=4390108, time=6.25 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 49.424215071345176604216766568584 y[1] (numeric) = 49.424215071345176604216766568602 absolute error = 1.8e-29 relative error = 3.6419394772413721657358728586142e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 49.910886523731884664292814557216 y[1] (numeric) = 49.910886523731884664292814557233 absolute error = 1.7e-29 relative error = 3.4060705357170429519002251561011e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 50.40244910553017387976148654122 y[1] (numeric) = 50.402449105530173879761486541238 absolute error = 1.8e-29 relative error = 3.5712550321339511794343750434182e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 50.89895197340786092983029148288 y[1] (numeric) = 50.898951973407860929830291482897 absolute error = 1.7e-29 relative error = 3.3399508911070789548644673065608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 51.400444778065487352279404612568 y[1] (numeric) = 51.400444778065487352279404612585 absolute error = 1.7e-29 relative error = 3.3073643765928155109855324463920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 51.906977669201430973337148919991 y[1] (numeric) = 51.906977669201430973337148920009 absolute error = 1.8e-29 relative error = 3.4677418736865022188217848814775e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 52.418601300526917537017237808153 y[1] (numeric) = 52.418601300526917537017237808171 absolute error = 1.8e-29 relative error = 3.4338955167464687813396771345014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 52.9353668348314340392599029227 y[1] (numeric) = 52.935366834831434039259902922718 absolute error = 1.8e-29 relative error = 3.4003731486670292981389875116192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 53.457325949099050312431513118509 y[1] (numeric) = 53.457325949099050312431513118527 absolute error = 1.8e-29 relative error = 3.3671717917838285058064536887918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 53.984530839676160496604750057851 y[1] (numeric) = 53.984530839676160496604750057869 absolute error = 1.8e-29 relative error = 3.3342884933938933964787082801824e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 54.517034227491161176072934038621 y[1] (numeric) = 54.51703422749116117607293403864 absolute error = 1.9e-29 relative error = 3.4851492325712245132497976567815e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 55.054889363326588153261897764787 y[1] (numeric) = 55.054889363326588153261897764806 absolute error = 1.9e-29 relative error = 3.4511012954021783782040521082132e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 55.598150033144239078110261202861 y[1] (numeric) = 55.59815003314423907811026120288 absolute error = 1.9e-29 relative error = 3.4173798927973960250906962104123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 56.146870563463814449618662535082 y[1] (numeric) = 56.146870563463814449618662535101 absolute error = 1.9e-29 relative error = 3.3839820116998256119837521021831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 56.701105826795614858150315907712 y[1] (numeric) = 56.701105826795614858150315907732 absolute error = 2.0e-29 relative error = 3.5272680679445352783561807091599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 57.260911247127837742734388822998 y[1] (numeric) = 57.260911247127837742734388823017 absolute error = 1.9e-29 relative error = 3.3181448891023411806883972933450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 57.826342805469022397620692052799 y[1] (numeric) = 57.826342805469022397620692052819 absolute error = 2.0e-29 relative error = 3.4586313139810852412877329778303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 58.397457045446197477205057110728 y[1] (numeric) = 58.397457045446197477205057110748 absolute error = 2.0e-29 relative error = 3.4248066631455469039591874086291e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 58.974311078959290818741032291737 y[1] (numeric) = 58.974311078959290818741032291757 absolute error = 2.0e-29 relative error = 3.3913071020401543355775633331218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 59.556962591892367028532192341085 y[1] (numeric) = 59.556962591892367028532192341105 absolute error = 2.0e-29 relative error = 3.3581296173627646082843204492176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 60.145469849882263960123061503388 y[1] (numeric) = 60.145469849882263960123061503409 absolute error = 2.1e-29 relative error = 3.4915347826551408921847902640468e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 60.739891704145204952943682133229 y[1] (numeric) = 60.73989170414520495294368213325 absolute error = 2.1e-29 relative error = 3.4573654003678197506278924924702e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=168072392, alloc=4390108, time=6.40 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 61.340287597361969497487219708124 y[1] (numeric) = 61.340287597361969497487219708145 absolute error = 2.1e-29 relative error = 3.4235248680025974157301129425905e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 61.946717569622210848991447239727 y[1] (numeric) = 61.946717569622210848991447239748 absolute error = 2.1e-29 relative error = 3.3900101286880939258849493499002e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 62.559242264428515026339091755126 y[1] (numeric) = 62.559242264428515026339091755147 absolute error = 2.1e-29 relative error = 3.3568181518625427221373270883619e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 63.177922934760801607080332059943 y[1] (numeric) = 63.177922934760801607080332059965 absolute error = 2.2e-29 relative error = 3.4822290727597650420917922384768e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 63.802821449201672763710634207787 y[1] (numeric) = 63.802821449201672763710634207809 absolute error = 2.2e-29 relative error = 3.4481233745306843449001398821709e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -2.000e+30 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 64.434000298123323081212027004718 y[1] (numeric) = 64.43400029812332308121202700474 absolute error = 2.2e-29 relative error = 3.4143464472499564049308251711730e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 65.071522599936628851995347043461 y[1] (numeric) = 65.071522599936628851995347043483 absolute error = 2.2e-29 relative error = 3.3808952243606214803962675572578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 65.71545210740304176238053926293 y[1] (numeric) = 65.715452107403041762380539262952 absolute error = 2.2e-29 relative error = 3.3477666659043854247729412873043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 66.365853214009918165243590001587 y[1] (numeric) = 66.365853214009918165243590001609 absolute error = 2.2e-29 relative error = 3.3149577583304197328476669376578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 67.022790960409921477070149341099 y[1] (numeric) = 67.022790960409921477070149341121 absolute error = 2.2e-29 relative error = 3.2824655143047246042041633873069e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 67.686331040925141645021734653992 y[1] (numeric) = 67.686331040925141645021734654014 absolute error = 2.2e-29 relative error = 3.2502869725200727051174801907145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 68.356539810116582101381339598584 y[1] (numeric) = 68.356539810116582101381339598606 absolute error = 2.2e-29 relative error = 3.2184191975065507624153195367248e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 69.033484289419671159548483832735 y[1] (numeric) = 69.033484289419671159548483832757 absolute error = 2.2e-29 relative error = 3.1868592794427155858443074606375e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 69.717232173846461408252914213396 y[1] (numeric) = 69.717232173846461408252914213418 absolute error = 2.2e-29 relative error = 3.1556043339673805887075971370533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 70.407851838755187329511563631169 y[1] (numeric) = 70.407851838755187329511563631191 absolute error = 2.2e-29 relative error = 3.1246515019920483598799202545181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -6.667e+29 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 71.105412346687858101731879995094 y[1] (numeric) = 71.105412346687858101731879995116 absolute error = 2.2e-29 relative error = 3.0939979495140043336200550876426e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 71.809983454276569352939848696489 y[1] (numeric) = 71.809983454276569352939848696511 absolute error = 2.2e-29 relative error = 3.0636408674300861067519775326919e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 72.521635619219224501063310332678 y[1] (numeric) = 72.5216356192192245010633103327 absolute error = 2.2e-29 relative error = 3.0335774713511424656386878338847e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 73.240440007325363259217722516329 y[1] (numeric) = 73.240440007325363259217722516352 absolute error = 2.3e-29 relative error = 3.1403415923907046036002494721500e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 73.96646849963280189471643767276 y[1] (numeric) = 73.966468499632801894716437672784 absolute error = 2.4e-29 relative error = 3.2447135150327131361544992484284e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 74.699793699595796911761951170653 y[1] (numeric) = 74.699793699595796911761951170676 absolute error = 2.3e-29 relative error = 3.0789911003628988296847753122322e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 75.440488940345450980176545280381 y[1] (numeric) = 75.440488940345450980176545280405 absolute error = 2.4e-29 relative error = 3.1813155425037070475221023468405e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=172074784, alloc=4390108, time=6.55 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 76.188628292023087156815560466137 y[1] (numeric) = 76.188628292023087156815560466161 absolute error = 2.4e-29 relative error = 3.1500764009046726058380643972197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 76.944286569187324743196600893995 y[1] (numeric) = 76.944286569187324743196600894019 absolute error = 2.4e-29 relative error = 3.1191399738848062449360180284551e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 77.70753933829559749310302086642 y[1] (numeric) = 77.707539338295597493103020866444 absolute error = 2.4e-29 relative error = 3.0885034070526013512235390122310e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 78.478462925260862328217071820222 y[1] (numeric) = 78.478462925260862328217071820246 absolute error = 2.4e-29 relative error = 3.0581638713867845577766928415376e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 79.257134423084254238951551456582 y[1] (numeric) = 79.257134423084254238951551456606 absolute error = 2.4e-29 relative error = 3.0281185630412868071731129131408e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 80.043631699564450642330605120616 y[1] (numeric) = 80.043631699564450642330605120641 absolute error = 2.5e-29 relative error = 3.1232965657823887795065843615735e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 80.838033405084516139779959223782 y[1] (numeric) = 80.838033405084516139779959223808 absolute error = 2.6e-29 relative error = 3.2163078324422304775594254175814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 81.640418980477006365791424660798 y[1] (numeric) = 81.640418980477006365791424660824 absolute error = 2.6e-29 relative error = 3.1846970317750919416303836578775e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 82.450868664968117444400811726181 y[1] (numeric) = 82.450868664968117444400811726207 absolute error = 2.6e-29 relative error = 3.1533930959113023461401331560851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 83.269463504201675475045050936085 y[1] (numeric) = 83.269463504201675475045050936111 absolute error = 2.6e-29 relative error = 3.1223931205811205617027293715537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 84.096285358343768453433785661304 y[1] (numeric) = 84.09628535834376845343378566133 absolute error = 2.6e-29 relative error = 3.0916942275406177525840415398897e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 84.931416910268831097381406177663 y[1] (numeric) = 84.931416910268831097381406177689 absolute error = 2.6e-29 relative error = 3.0612935643672758913787973072229e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 85.774941673828001192903868431231 y[1] (numeric) = 85.774941673828001192903868431258 absolute error = 2.7e-29 relative error = 3.1477724698049371839415060751534e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 86.626944002200574303105227123016 y[1] (numeric) = 86.626944002200574303105227123043 absolute error = 2.7e-29 relative error = 3.1168131706590182960750391642527e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 87.4875090963293919922843405557 y[1] (numeric) = 87.487509096329391992284340555728 absolute error = 2.8e-29 relative error = 3.2004568754118023304795998614792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 88.356723013441007111113671531353 y[1] (numeric) = 88.356723013441007111113671531382 absolute error = 2.9e-29 relative error = 3.2821497913167807424814849345847e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 89.234672675651478166518863585011 y[1] (numeric) = 89.23467267565147816651886358504 absolute error = 2.9e-29 relative error = 3.2498578333344325070926508820687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 90.121445878658653362867599725013 y[1] (numeric) = 90.121445878658653362867599725043 absolute error = 3.0e-29 relative error = 3.3288413992372703177097986704246e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 91.017131300521813550115456745574 y[1] (numeric) = 91.017131300521813550115456745604 absolute error = 3.0e-29 relative error = 3.2960827891779540115906135490725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 91.92181851052955205051996320841 y[1] (numeric) = 91.92181851052955205051996320844 absolute error = 3.0e-29 relative error = 3.2636430051221767452658766652161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 92.835597978156778159295456987861 y[1] (numeric) = 92.835597978156778159295456987891 absolute error = 3.0e-29 relative error = 3.2315190135424860051557294887603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 93.758561082111740027023002329753 y[1] (numeric) = 93.758561082111740027023002329783 absolute error = 3.0e-29 relative error = 3.1997078084129984063338637490120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=176075680, alloc=4390108, time=6.71 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 94.690800119473971633642818281708 y[1] (numeric) = 94.690800119473971633642818281737 absolute error = 2.9e-29 relative error = 3.0625995306207051852282804543815e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.000e+16 Order of pole (six term test) = -14 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 95.632408314924077656341598932635 y[1] (numeric) = 95.632408314924077656341598932665 absolute error = 3.0e-29 relative error = 3.1370118695754208173547698481061e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 96.583479830066279217513027221686 y[1] (numeric) = 96.583479830066279217513027221715 absolute error = 2.9e-29 relative error = 3.0025838840166066844192535781206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 97.54410977284465277513509238733 y[1] (numeric) = 97.54410977284465277513509238736 absolute error = 3.0e-29 relative error = 3.0755316820115890865006131533809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 98.51439420705400378730014068658 y[1] (numeric) = 98.51439420705400378730014068661 absolute error = 3.0e-29 relative error = 3.0452402657978164132264776789400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 99.494430161946326246189866862324 y[1] (numeric) = 99.494430161946326246189866862355 absolute error = 3.1e-29 relative error = 3.1157523038768638696059638217712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 100.48431564193380873545405348757 y[1] (numeric) = 100.4843156419338087354540534876 absolute error = 3e-29 relative error = 2.9855405600712964718847115348311e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 101.48414963638935731968466139449 y[1] (numeric) = 101.48414963638935731968466139453 absolute error = 4e-29 relative error = 3.9415022092925067751637193043035e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 102.49403212954561532644134822903 y[1] (numeric) = 102.49403212954561532644134822907 absolute error = 4e-29 relative error = 3.9026662498205427146554496179528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 103.51406411049346993105582833176 y[1] (numeric) = 103.5140641104934699310558283318 absolute error = 4e-29 relative error = 3.8642092109631606748734455838612e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 104.54434758328104540320567097554 y[1] (numeric) = 104.54434758328104540320567097558 absolute error = 4e-29 relative error = 3.8261274688366686161522124380556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 105.58498557711419292299805009791 y[1] (numeric) = 105.58498557711419292299805009795 absolute error = 4e-29 relative error = 3.7884174327784441208818848887336e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 106.63608215665949702404549041811 y[1] (numeric) = 106.63608215665949702404549041816 absolute error = 5e-29 relative error = 4.6888444313384281106888871963906e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 107.69774243245082897276378483542 y[1] (numeric) = 107.69774243245082897276378483546 absolute error = 4e-29 relative error = 3.7140982806662290063571859641367e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 108.77007257140048774790216962363 y[1] (numeric) = 108.77007257140048774790216962368 absolute error = 5e-29 relative error = 4.5968526836440462635764269311536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 109.85317980741597974316302378673 y[1] (numeric) = 109.85317980741597974316302378678 absolute error = 5e-29 relative error = 4.5515296041184412638681836556445e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.774e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 110.94717245212349887972870045537 y[1] (numeric) = 110.94717245212349887972870045541 absolute error = 4e-29 relative error = 3.6053194611391298072076912660271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 112.05215990569917948564300622207 y[1] (numeric) = 112.05215990569917948564300622211 absolute error = 4e-29 relative error = 3.5697660833725282110255788635110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 113.1682526678092050763613407161 y[1] (numeric) = 113.16825266780920507636134071615 absolute error = 5e-29 relative error = 4.4182002303038595694893558957638e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 114.29556234865986705646433913828 y[1] (numeric) = 114.29556234865986705646433913832 absolute error = 4e-29 relative error = 3.4996984290588256697721364528658e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 115.43420168015867835761360206601 y[1] (numeric) = 115.43420168015867835761360206605 absolute error = 4e-29 relative error = 3.4651775139252658911206908959668e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 116.58428452718765813341426713653 y[1] (numeric) = 116.58428452718765813341426713657 absolute error = 4e-29 relative error = 3.4309941654847939952923967596822e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=180076540, alloc=4390108, time=6.86 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 117.74592589898991484904834409238 y[1] (numeric) = 117.74592589898991484904834409242 absolute error = 4e-29 relative error = 3.3971451406577406332341385774294e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 118.91924196067066643347662739359 y[1] (numeric) = 118.91924196067066643347662739364 absolute error = 5e-29 relative error = 4.2045340329814877349699951381052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 120.10435004481384760580862199534 y[1] (numeric) = 120.10435004481384760580862199539 absolute error = 5e-29 relative error = 4.1630465492168923637445831271902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 121.30136866321546604625365765727 y[1] (numeric) = 121.30136866321546604625365765732 absolute error = 5e-29 relative error = 4.1219650323007819670778640852655e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 122.51041751873488075704811629788 y[1] (numeric) = 122.51041751873488075704811629793 absolute error = 5e-29 relative error = 4.0812855765799475900677125165314e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 123.73161751726518775107096333766 y[1] (numeric) = 123.73161751726518775107096333771 absolute error = 5e-29 relative error = 4.0410043126626975666829139821401e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 124.96509077982391011669179924248 y[1] (numeric) = 124.96509077982391011669179924253 absolute error = 5e-29 relative error = 4.0011174071081209860528705311807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 126.21096065476520153793352471171 y[1] (numeric) = 126.21096065476520153793352471176 absolute error = 5e-29 relative error = 3.9616210621174927030561975215969e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 127.46935173011478450047850596726 y[1] (numeric) = 127.46935173011478450047850596731 absolute error = 5e-29 relative error = 3.9225115152278162172395272411631e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.000e+15 Order of pole (six term test) = -5.000e+29 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 128.74038984602885668761799019549 y[1] (numeric) = 128.74038984602885668761799019554 absolute error = 5e-29 relative error = 3.8837850390075004653590765754106e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 130.0242021073782114671668226883 y[1] (numeric) = 130.02420210737821146716682268836 absolute error = 6e-29 relative error = 4.6145255289049995625937325764961e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 131.32091689645883089187895918358 y[1] (numeric) = 131.32091689645883089187895918364 absolute error = 6e-29 relative error = 4.5689598746334938174978331404115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 132.63066388583022228325601109699 y[1] (numeric) = 132.63066388583022228325601109705 absolute error = 6e-29 relative error = 4.5238407350240355514140069609247e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 133.95357405128278224310585398182 y[1] (numeric) = 133.95357405128278224310585398188 absolute error = 6e-29 relative error = 4.4791638017086130014401484411752e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 135.28977968493548484005862777435 y[1] (numeric) = 135.28977968493548484005862777441 absolute error = 6e-29 relative error = 4.4349248065691838212207653368866e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 136.63941440846520375077355696288 y[1] (numeric) = 136.63941440846520375077355696294 absolute error = 6e-29 relative error = 4.3911195213877342155635992394432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.732e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 138.00261318646899129907518322816 y[1] (numeric) = 138.00261318646899129907518322822 absolute error = 6e-29 relative error = 4.3477437574988569753555115311410e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 139.37951233996065063205819382868 y[1] (numeric) = 139.37951233996065063205819382874 absolute error = 6e-29 relative error = 4.3047933654448413239300499559873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 140.77024956000295070162563718432 y[1] (numeric) = 140.77024956000295070162563718438 absolute error = 6e-29 relative error = 4.2622642346332672320226152505882e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 142.17496392147684728431889649845 y[1] (numeric) = 142.17496392147684728431889649851 absolute error = 6e-29 relative error = 4.2201522929970966124981245140926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 143.59379589698908697301579351366 y[1] (numeric) = 143.59379589698908697301579351371 absolute error = 5e-29 relative error = 3.4820445888810446399878325310093e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 145.02688737091958491248570083683 y[1] (numeric) = 145.02688737091958491248570083689 absolute error = 6e-29 relative error = 4.1371638795876856342397163284808e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=184077460, alloc=4390108, time=7.02 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 146.47438165360998102828140547844 y[1] (numeric) = 146.47438165360998102828140547849 absolute error = 5e-29 relative error = 3.4135662110690814494335035558578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 147.93642349569479361641444906234 y[1] (numeric) = 147.93642349569479361641444906239 absolute error = 5e-29 relative error = 3.3798302553566253194622954099052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.414e+16 Order of pole (six term test) = -1.000e+30 Finished! diff ( y , x , 2 ) = diff ( y , x , 1 ) ; Iterations = 1000 Total Elapsed Time = 6 Seconds Elapsed Time(since restart) = 6 Seconds Time to Timeout = 2 Minutes 53 Seconds Percent Done = 100.1 % > quit bytes used=184512676, alloc=4390108, time=7.04