|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp3[1] := sin(array_x[1]); > array_tmp3_g[1] := cos(array_x[1]); > #emit pre add FULL FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp2[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3_g[1] * array_x[2] / 1; > array_tmp3_g[2] := -array_tmp3[1] * array_x[2] / 1; > #emit pre add FULL FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp2[2] + array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3_g[2] * array_x[2] / 2; > array_tmp3_g[3] := -array_tmp3[2] * array_x[2] / 2; > #emit pre add FULL FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp2[3] + array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3_g[3] * array_x[2] / 3; > array_tmp3_g[4] := -array_tmp3[3] * array_x[2] / 3; > #emit pre add FULL FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp2[4] + array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3_g[4] * array_x[2] / 4; > array_tmp3_g[5] := -array_tmp3[4] * array_x[2] / 4; > #emit pre add FULL FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp2[5] + array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit sin LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_x[2] / (kkk - 1); > #emit FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := sin(array_x[1]); array_tmp3_g[1] := cos(array_x[1]); array_tmp4[1] := array_tmp2[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3_g[1]*array_x[2]; array_tmp3_g[2] := -array_tmp3[1]*array_x[2]; array_tmp4[2] := array_tmp2[2] + array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := 1/2*array_tmp3_g[2]*array_x[2]; array_tmp3_g[3] := -1/2*array_tmp3[2]*array_x[2]; array_tmp4[3] := array_tmp2[3] + array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := 1/3*array_tmp3_g[3]*array_x[2]; array_tmp3_g[4] := -1/3*array_tmp3[3]*array_x[2]; array_tmp4[4] := array_tmp2[4] + array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := 1/4*array_tmp3_g[4]*array_x[2]; array_tmp3_g[5] := -1/4*array_tmp3[4]*array_x[2]; array_tmp4[5] := array_tmp2[5] + array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(2.0 - cos(x) - cos(x)); > end; exact_soln_y := proc(x) return 2.0 - 2*cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > 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/addpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"Digits:=32;"); > 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,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > 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(2.0 - cos(x) - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > max_terms:=30; > Digits:=32; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3_g:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_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); > glob_look_poles := true; > glob_max_iter := 100; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-25T23:50:52-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"add") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"add diffeq.mxt") > ; > logitem_str(html_log_file,"add maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, 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/addpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "Digits:=32;"); 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, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); 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(2.0 - cos(x) - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; max_terms := 30; Digits := 32; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3_g := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_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); glob_look_poles := true; glob_max_iter := 100; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-25T23:50:52-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "add"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "add diffeq.mxt"); logitem_str(html_log_file, "add 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/addpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK max_terms:=30; Digits:=32; ! #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); glob_look_poles := true; glob_max_iter := 100; 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(2.0 - cos(x) - cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 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 = 1.4067353021209587373088533999590e-183 estimated_step_error = 1.4067353021209587373088533999590e-183 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.4404402164116865043464570617934e-176 estimated_step_error = 9.4404402164116865043464570617934e-176 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.3353713926173167972978718673577e-168 estimated_step_error = 6.3353713926173167972978718673577e-168 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.2515947071303265754442581571220e-160 estimated_step_error = 4.2515947071303265754442581571220e-160 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8531954809087672667810583490172e-152 estimated_step_error = 2.8531954809087672667810583490172e-152 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9147451570588862570582253255205e-144 estimated_step_error = 1.9147451570588862570582253255205e-144 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2849611492638689738777494471502e-136 estimated_step_error = 1.2849611492638689738777494471502e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.6231937516725606723920452632870e-129 estimated_step_error = 8.6231937516725606723920452632870e-129 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.7868809957316295545604444322444e-121 estimated_step_error = 5.7868809957316295545604444322444e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.8834478583206815928292968901601e-113 estimated_step_error = 3.8834478583206815928292968901601e-113 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 = 2.6060542057122508356940820194223e-105 estimated_step_error = 2.6060542057122508356940820194223e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7487812515942845088201533601559e-97 estimated_step_error = 1.7487812515942845088201533601559e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1734367429771466736806510441436e-89 estimated_step_error = 1.1734367429771466736806510441436e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.8727807875006785840587221469819e-82 estimated_step_error = 7.8727807875006785840587221469819e-82 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.2806225223138969085011158615030e-74 estimated_step_error = 5.2806225223138969085011158615030e-74 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 = 3.5401263640216604856691597924428e-66 estimated_step_error = 3.5401263640216604856691597924428e-66 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 = 2.3708525684792538752954511718038e-58 estimated_step_error = 2.3708525684792538752954511718038e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5844909190829553189763380039629e-50 estimated_step_error = 1.5844909190829553189763380039629e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = 1.4326756290735474710667216569729 y[1] (numeric) = 1.4326756290735474710667216569729 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.99 y[1] (analytic) = 1.4518821609091455120738168046061 y[1] (numeric) = 1.4518821609091455120738168046061 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.98 y[1] (analytic) = 1.4711435040718892951674933586384 y[1] (numeric) = 1.4711435040718892951674933586384 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.97 y[1] (analytic) = 1.4904577324435136117680929719749 y[1] (numeric) = 1.4904577324435136117680929719749 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=4000360, alloc=3145152, time=0.14 x[1] = -4.96 y[1] (analytic) = 1.5098229146172764361031039541294 y[1] (numeric) = 1.5098229146172764361031039541293 absolute error = 1e-31 relative error = 6.6232933035957335552074366499358e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.95 y[1] (analytic) = 1.5292371140910979899094851767305 y[1] (numeric) = 1.5292371140910979899094851767305 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.94 y[1] (analytic) = 1.5486983894612093366651383919206 y[1] (numeric) = 1.5486983894612093366651383919205 absolute error = 1e-31 relative error = 6.4570351903568455788146775456171e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.93 y[1] (analytic) = 1.5682047946162911406514791070285 y[1] (numeric) = 1.5682047946162911406514791070284 absolute error = 1e-31 relative error = 6.3767181648279574693005125015443e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.92 y[1] (analytic) = 1.5877543789320831771329815183765 y[1] (numeric) = 1.5877543789320831771329815183764 absolute error = 1e-31 relative error = 6.2982033825193776798338310355874e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.91 y[1] (analytic) = 1.6073451874664451328648536009612 y[1] (numeric) = 1.6073451874664451328648536009612 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = 1.6269752611548491910113417117562 y[1] (numeric) = 1.6269752611548491910113417117562 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.89 y[1] (analytic) = 1.6466426370062848513790828205723 y[1] (numeric) = 1.6466426370062848513790828205724 absolute error = 1e-31 relative error = 6.0729631161383757667052432978067e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.88 y[1] (analytic) = 1.6663453482995563956467345059368 y[1] (numeric) = 1.6663453482995563956467345059368 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.87 y[1] (analytic) = 1.6860814247799533680079404287439 y[1] (numeric) = 1.686081424779953368007940428744 absolute error = 1e-31 relative error = 5.9309116707131016153521868418806e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.86 y[1] (analytic) = 1.7058488928562744043434585080292 y[1] (numeric) = 1.7058488928562744043434585080293 absolute error = 1e-31 relative error = 5.8621839495150089357840100419421e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.85 y[1] (analytic) = 1.7256457757981847077037205630694 y[1] (numeric) = 1.7256457757981847077037205630695 absolute error = 1e-31 relative error = 5.7949320423970405291180884372253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.84 y[1] (analytic) = 1.7454700939338874345187391805346 y[1] (numeric) = 1.7454700939338874345187391805347 absolute error = 1e-31 relative error = 5.7291156318022636556024786906784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.83 y[1] (analytic) = 1.7653198648480892245614664220924 y[1] (numeric) = 1.7653198648480892245614664220924 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.82 y[1] (analytic) = 1.7851931035802400782765787616605 y[1] (numeric) = 1.7851931035802400782765787616605 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.81 y[1] (analytic) = 1.8050878228230277576521547209232 y[1] (numeric) = 1.8050878228230277576521547209233 absolute error = 1e-31 relative error = 5.5398966596321712233003319840919e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8 y[1] (analytic) = 1.825002033121106861359569484701 y[1] (numeric) = 1.8250020331211068613595694847011 absolute error = 1e-31 relative error = 5.4794459504782379050358995417346e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.79 y[1] (analytic) = 1.8449337430700427014196995173048 y[1] (numeric) = 1.8449337430700427014196995173049 absolute error = 1e-31 relative error = 5.4202488504327556917303717753508e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.78 y[1] (analytic) = 1.8648809595154500871735565706809 y[1] (numeric) = 1.864880959515450087173556570681 absolute error = 1e-31 relative error = 5.3622725616750833802878716448076e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.77 y[1] (analytic) = 1.8848416877523071028449024544255 y[1] (numeric) = 1.8848416877523071028449024544256 absolute error = 1e-31 relative error = 5.3054853704584079860519453085827e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.76 y[1] (analytic) = 1.9048139317244239474831825671789 y[1] (numeric) = 1.9048139317244239474831825671791 absolute error = 2e-31 relative error = 1.0499713209202561375821943934823e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9247956942240468905690073752533 y[1] (numeric) = 1.9247956942240468905690073752535 absolute error = 2e-31 relative error = 1.0390713185828642559255802306881e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.944784977091577383052957365562 y[1] (numeric) = 1.9447849770915773830529573655622 absolute error = 2e-31 relative error = 1.0283913252924220905658288514537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9647797814153863520830396301143 y[1] (numeric) = 1.9647797814153863520830396301145 absolute error = 2e-31 relative error = 1.0179257843132128209552597794626e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=8001788, alloc=4259060, time=0.30 x[1] = -4.72 y[1] (analytic) = 1.9847781077317036981578346936507 y[1] (numeric) = 1.9847781077317036981578346936509 absolute error = 2e-31 relative error = 1.0076693168918980998766221861335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.71 y[1] (analytic) = 2.0047779562245630059221922954494 y[1] (numeric) = 2.0047779562245630059221922954496 absolute error = 2e-31 relative error = 9.9761671550221903557712361455900e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002304 Order of pole (three term test) = -0.893 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.7 y[1] (analytic) = 2.0247773269257814743010165926542 y[1] (numeric) = 2.0247773269257814743010165926544 absolute error = 2e-31 relative error = 9.8776293738758874839623492773220e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01195 Order of pole (three term test) = -0.8966 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.69 y[1] (analytic) = 2.044774219914955068144776792884 y[1] (numeric) = 2.0447742199149550681447767928842 absolute error = 2e-31 relative error = 9.7810309838666819231987230180752e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02158 Order of pole (three term test) = -0.905 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.68 y[1] (analytic) = 2.0647666355194488920382407358891 y[1] (numeric) = 2.0647666355194488920382407358893 absolute error = 2e-31 relative error = 9.6863246702785127976950039258927e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03121 Order of pole (three term test) = -0.9182 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.67 y[1] (analytic) = 2.0847525745143627874017086402106 y[1] (numeric) = 2.0847525745143627874017086402107 absolute error = 1e-31 relative error = 4.7967322943968406903304045188291e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04083 Order of pole (three term test) = -0.9363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.66 y[1] (analytic) = 2.1047300383224521564916743335919 y[1] (numeric) = 2.1047300383224521564916743335921 absolute error = 2e-31 relative error = 9.5024063114245004152029273785685e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05043 Order of pole (three term test) = -0.9592 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.65 y[1] (analytic) = 2.1246970292139840213851140323542 y[1] (numeric) = 2.1246970292139840213851140323543 absolute error = 1e-31 relative error = 4.7065533873784471599150664009714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06 Order of pole (three term test) = -0.9868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.64 y[1] (analytic) = 2.1446515505065083325080504015202 y[1] (numeric) = 2.1446515505065083325080504015204 absolute error = 2e-31 relative error = 9.3255242303937645592356643111852e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06956 Order of pole (three term test) = -1.019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.63 y[1] (analytic) = 2.1645916067645245497440145748052 y[1] (numeric) = 2.1645916067645245497440145748054 absolute error = 2e-31 relative error = 9.2396181974920238408038097776135e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07909 Order of pole (three term test) = -1.057 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.62 y[1] (analytic) = 2.1845152039990235296306835512316 y[1] (numeric) = 2.1845152039990235296306835512318 absolute error = 2e-31 relative error = 9.1553494172929271713261672307516e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08858 Order of pole (three term test) = -1.099 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.61 y[1] (analytic) = 2.2044203498668847646222576563454 y[1] (numeric) = 2.2044203498668847646222576563455 absolute error = 1e-31 relative error = 4.5363399047753555505771014786574e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09804 Order of pole (three term test) = -1.145 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6 y[1] (analytic) = 2.2243050538701090348598156424584 y[1] (numeric) = 2.2243050538701090348598156424585 absolute error = 1e-31 relative error = 4.4957862153848084591819074827995e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1075 Order of pole (three term test) = -1.197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.59 y[1] (analytic) = 2.244167327554866549350497048793 y[1] (numeric) = 2.2441673275548665493504970487931 absolute error = 1e-31 relative error = 4.4559957170820698935084701819744e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1168 Order of pole (three term test) = -1.253 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.58 y[1] (analytic) = 2.2640051847103406719072668013646 y[1] (numeric) = 2.2640051847103406719072668013647 absolute error = 1e-31 relative error = 4.4169510156309165269893879563386e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1262 Order of pole (three term test) = -1.314 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.57 y[1] (analytic) = 2.2838166415673473476423706287492 y[1] (numeric) = 2.2838166415673473476423706287493 absolute error = 1e-31 relative error = 4.3786352275361115198056476191367e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1355 Order of pole (three term test) = -1.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.56 y[1] (analytic) = 2.3035997169967103682373475852198 y[1] (numeric) = 2.3035997169967103682373475852199 absolute error = 1e-31 relative error = 4.3410319623746856002179814072745e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1447 Order of pole (three term test) = -1.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.55 y[1] (analytic) = 2.3233524327073726386283848500159 y[1] (numeric) = 2.323352432707372638628384850016 absolute error = 1e-31 relative error = 4.3041253058396865402557992080671e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1538 Order of pole (three term test) = -1.525 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.54 y[1] (analytic) = 2.3430728134442236341454384391956 y[1] (numeric) = 2.3430728134442236341454384391957 absolute error = 1e-31 relative error = 4.2678998034638106823258605856865e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.163 Order of pole (three term test) = -1.604 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.53 y[1] (analytic) = 2.3627588871856232655242615827628 y[1] (numeric) = 2.3627588871856232655242615827629 absolute error = 1e-31 relative error = 4.2323404449919985194791392336668e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.172 Order of pole (three term test) = -1.688 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.52 y[1] (analytic) = 2.3824086853406023995694422363978 y[1] (numeric) = 2.3824086853406023995694422363979 absolute error = 1e-31 relative error = 4.1974326493736503347208933691486e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.181 Order of pole (three term test) = -1.777 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.51 y[1] (analytic) = 2.4020202429457203155807166434815 y[1] (numeric) = 2.4020202429457203155807166434817 absolute error = 2e-31 relative error = 8.3263245006932068000353543773883e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1899 Order of pole (three term test) = -1.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.5 y[1] (analytic) = 2.4215915988615594119609636495877 y[1] (numeric) = 2.4215915988615594119609636495878 absolute error = 1e-31 relative error = 4.1295154825864146680687126966162e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1987 Order of pole (three term test) = -1.967 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.49 y[1] (analytic) = 2.4411207959688375136989640130322 y[1] (numeric) = 2.4411207959688375136989640130323 absolute error = 1e-31 relative error = 4.0964789683958173406733440034490e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2074 Order of pole (three term test) = -2.069 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=12002816, alloc=4324584, time=0.45 x[1] = -4.48 y[1] (analytic) = 2.4606058813641181696596028136977 y[1] (numeric) = 2.4606058813641181696596028136978 absolute error = 1e-31 relative error = 4.0640397049104709106496876647709e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2161 Order of pole (three term test) = -2.175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.47 y[1] (analytic) = 2.4800449065550993688148773106603 y[1] (numeric) = 2.4800449065550993688148773106604 absolute error = 1e-31 relative error = 4.0321850517983066806621672466604e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2247 Order of pole (three term test) = -2.286 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.46 y[1] (analytic) = 2.4994359276554611467068272022253 y[1] (numeric) = 2.4994359276554611467068272022254 absolute error = 1e-31 relative error = 4.0009027194308885020917627543848e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2332 Order of pole (three term test) = -2.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.45 y[1] (analytic) = 2.5187770055792525975441134594889 y[1] (numeric) = 2.518777005579252597544113459489 absolute error = 1e-31 relative error = 3.9701807575062654200683556442469e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2415 Order of pole (three term test) = -2.519 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.44 y[1] (analytic) = 2.5380662062347988533930247123268 y[1] (numeric) = 2.5380662062347988533930247123269 absolute error = 1e-31 relative error = 3.9400075441037926755660692309145e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2498 Order of pole (three term test) = -2.643 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.43 y[1] (analytic) = 2.5573016007181086399265806978673 y[1] (numeric) = 2.5573016007181086399265806978674 absolute error = 1e-31 relative error = 3.9103717751523434869543981799336e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.258 Order of pole (three term test) = -2.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.42 y[1] (analytic) = 2.5764812655057630681373302869864 y[1] (numeric) = 2.5764812655057630681373302869865 absolute error = 1e-31 relative error = 3.8812624542942293791024037924885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2661 Order of pole (three term test) = -2.901 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.41 y[1] (analytic) = 2.5956032826472663732954129329813 y[1] (numeric) = 2.5956032826472663732954129329813 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2741 Order of pole (three term test) = -3.037 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4 y[1] (analytic) = 2.6146657399568393662382794844354 y[1] (numeric) = 2.6146657399568393662382794844355 absolute error = 1e-31 relative error = 3.8245806518140522714789189995086e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.282 Order of pole (three term test) = -3.176 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.39 y[1] (analytic) = 2.6336667312046364178067707335115 y[1] (numeric) = 2.6336667312046364178067707335116 absolute error = 1e-31 relative error = 3.7969876300278928696899242934907e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2897 Order of pole (three term test) = -3.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.38 y[1] (analytic) = 2.6526043563073668548884570476882 y[1] (numeric) = 2.6526043563073668548884570476883 absolute error = 1e-31 relative error = 3.7698799582463114427332273735060e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2974 Order of pole (three term test) = -3.467 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.37 y[1] (analytic) = 2.6714767215183017060874853848457 y[1] (numeric) = 2.6714767215183017060874853848458 absolute error = 1e-31 relative error = 3.7432480393527891628200396906084e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3049 Order of pole (three term test) = -3.618 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.36 y[1] (analytic) = 2.6902819396166467965047051339269 y[1] (numeric) = 2.690281939616646796504705133927 absolute error = 1e-31 relative error = 3.7170825305488076449497641324066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3123 Order of pole (three term test) = -3.772 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.35 y[1] (analytic) = 2.7090181300962632544764051548717 y[1] (numeric) = 2.7090181300962632544764051548719 absolute error = 2e-31 relative error = 7.3827486711169823680496829818369e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3196 Order of pole (three term test) = -3.931 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.34 y[1] (analytic) = 2.7276834193537165583782547088473 y[1] (numeric) = 2.7276834193537165583782547088475 absolute error = 2e-31 relative error = 7.3322291942291082732782180464257e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3267 Order of pole (three term test) = -4.093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.33 y[1] (analytic) = 2.7462759408756353187464749013257 y[1] (numeric) = 2.7462759408756353187464749013259 absolute error = 2e-31 relative error = 7.2825893794281675596825582109261e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3338 Order of pole (three term test) = -4.258 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.32 y[1] (analytic) = 2.7647938354253610599941603188602 y[1] (numeric) = 2.7647938354253610599941603188603 absolute error = 1e-31 relative error = 3.6169062126332139117688940876409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3406 Order of pole (three term test) = -4.428 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.31 y[1] (analytic) = 2.7832352512288703369001201936885 y[1] (numeric) = 2.7832352512288703369001201936886 absolute error = 1e-31 relative error = 3.5929409831902428670105256687859e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3474 Order of pole (three term test) = -4.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.3 y[1] (analytic) = 2.8015983441599505938135247926721 y[1] (numeric) = 2.8015983441599505938135247926722 absolute error = 1e-31 relative error = 3.5693910302472229706455336380633e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.354 Order of pole (three term test) = -4.776 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.29 y[1] (analytic) = 2.8198812779246112491427492675585 y[1] (numeric) = 2.8198812779246112491427492675586 absolute error = 1e-31 relative error = 3.5462485879404981287563707948899e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3605 Order of pole (three term test) = -4.955 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.28 y[1] (analytic) = 2.8380822242447115641736414736721 y[1] (numeric) = 2.8380822242447115641736414736722 absolute error = 1e-31 relative error = 3.5235060896310935470032471212809e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3668 Order of pole (three term test) = -5.137 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.27 y[1] (analytic) = 2.8561993630407869335833546441886 y[1] (numeric) = 2.8561993630407869335833546441887 absolute error = 1e-31 relative error = 3.5011561620662677026697629336598e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.373 Order of pole (three term test) = -5.323 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.26 y[1] (analytic) = 2.874230882614055315173048270972 y[1] (numeric) = 2.8742308826140553151730482709721 absolute error = 1e-31 relative error = 3.4791916197439228173287427509077e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.379 Order of pole (three term test) = -5.511 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.25 y[1] (analytic) = 2.8921749798275855983281554410897 y[1] (numeric) = 2.8921749798275855983281554410898 absolute error = 1e-31 relative error = 3.4576054594719372672645682229952e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3849 Order of pole (three term test) = -5.703 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.24 y[1] (analytic) = 2.9100298602866097945203437394119 y[1] (numeric) = 2.910029860286609794520343739412 absolute error = 1e-31 relative error = 3.4363908551148326440622672861197e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3906 Order of pole (three term test) = -5.897 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16006156, alloc=4390108, time=0.61 TOP MAIN SOLVE Loop x[1] = -4.23 y[1] (analytic) = 2.9277937385179610187823791790897 y[1] (numeric) = 2.9277937385179610187823791790898 absolute error = 1e-31 relative error = 3.4155411525205204960880784747755e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3962 Order of pole (three term test) = -6.094 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.22 y[1] (analytic) = 2.9454648381486193185072768263104 y[1] (numeric) = 2.9454648381486193185072768263105 absolute error = 1e-31 relative error = 3.3950498646201900451347112316034e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4016 Order of pole (three term test) = -6.294 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.21 y[1] (analytic) = 2.9630413920833474951376458989737 y[1] (numeric) = 2.9630413920833474951376458989738 absolute error = 1e-31 relative error = 3.3749106666946992313962498559020e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4068 Order of pole (three term test) = -6.497 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.2 y[1] (analytic) = 2.9805216426813991553110897627543 y[1] (numeric) = 2.9805216426813991553110897627544 absolute error = 1e-31 relative error = 3.3551173918011180954401442753502e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4119 Order of pole (three term test) = -6.702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.19 y[1] (analytic) = 2.9979038419322813208038025029849 y[1] (numeric) = 2.997903841932281320803802502985 absolute error = 1e-31 relative error = 3.3356640263533465134092578897236e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4168 Order of pole (three term test) = -6.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.18 y[1] (analytic) = 3.0151862516305540211578360660934 y[1] (numeric) = 3.0151862516305540211578360660936 absolute error = 2e-31 relative error = 6.6330894117019767475557692735683e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4216 Order of pole (three term test) = -7.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.17 y[1] (analytic) = 3.0323671435496493891784410855156 y[1] (numeric) = 3.0323671435496493891784410855157 absolute error = 1e-31 relative error = 3.2977537107509120927131822853741e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4262 Order of pole (three term test) = -7.332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.16 y[1] (analytic) = 3.0494447996146928775367804214184 y[1] (numeric) = 3.0494447996146928775367804214186 absolute error = 2e-31 relative error = 6.5585709249523270893653551616871e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4306 Order of pole (three term test) = -7.547 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.15 y[1] (analytic) = 3.0664175120743093145003723433254 y[1] (numeric) = 3.0664175120743093145003723433256 absolute error = 2e-31 relative error = 6.5222690391142452680841649927287e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4348 Order of pole (three term test) = -7.764 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.14 y[1] (analytic) = 3.0832835836713966183288615471946 y[1] (numeric) = 3.0832835836713966183288615471948 absolute error = 2e-31 relative error = 6.4865911478000188342990761526171e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4389 Order of pole (three term test) = -7.983 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.13 y[1] (analytic) = 3.100041327812850093105989384141 y[1] (numeric) = 3.1000413278128500931059893841412 absolute error = 2e-31 relative error = 6.4515268943561008737632383399972e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4428 Order of pole (three term test) = -8.204 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.12 y[1] (analytic) = 3.1166890687382203337196165455186 y[1] (numeric) = 3.1166890687382203337196165455188 absolute error = 2e-31 relative error = 6.4170661746816225130821004523842e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4465 Order of pole (three term test) = -8.427 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.11 y[1] (analytic) = 3.1332251416872878743398479877489 y[1] (numeric) = 3.1332251416872878743398479877492 absolute error = 3e-31 relative error = 9.5747986957121626636379778548214e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.45 Order of pole (three term test) = -8.652 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.1 y[1] (analytic) = 3.1496478930665378230700573593196 y[1] (numeric) = 3.1496478930665378230700573593198 absolute error = 2e-31 relative error = 6.3499161426986500307154861151519e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4534 Order of pole (three term test) = -8.878 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.09 y[1] (analytic) = 3.1659556806145178354460742272886 y[1] (numeric) = 3.1659556806145178354460742272888 absolute error = 2e-31 relative error = 6.3172078252586161032927262322998e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4565 Order of pole (three term test) = -9.106 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.08 y[1] (analytic) = 3.1821468735660628911239820364958 y[1] (numeric) = 3.1821468735660628911239820364961 absolute error = 3e-31 relative error = 9.4275975283254585611840122620044e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4595 Order of pole (three term test) = -9.336 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.07 y[1] (analytic) = 3.1982198528153704514157115460792 y[1] (numeric) = 3.1982198528153704514157115460795 absolute error = 3e-31 relative error = 9.3802181778063852972369531862489e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4623 Order of pole (three term test) = -9.567 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.06 y[1] (analytic) = 3.2141730110779096902925716955787 y[1] (numeric) = 3.214173011077909690292571695579 absolute error = 3e-31 relative error = 9.3336606015303316829570607780944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4649 Order of pole (three term test) = -9.799 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.05 y[1] (analytic) = 3.2300047530511486080685414569647 y[1] (numeric) = 3.2300047530511486080685414569651 absolute error = 4e-31 relative error = 1.2383882705502192688918770621852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4674 Order of pole (three term test) = -10.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.04 y[1] (analytic) = 3.2457134955740829551858931583454 y[1] (numeric) = 3.2457134955740829551858931583457 absolute error = 3e-31 relative error = 9.2429599965950704501383320622772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4696 Order of pole (three term test) = -10.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.03 y[1] (analytic) = 3.2612976677855510133437090437049 y[1] (numeric) = 3.2612976677855510133437090437052 absolute error = 3e-31 relative error = 9.1987923385019486345928346778274e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4717 Order of pole (three term test) = -10.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.02 y[1] (analytic) = 3.2767557112813184026231067615307 y[1] (numeric) = 3.276755711281318402623106761531 absolute error = 3e-31 relative error = 9.1553971804230169814521462479381e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4736 Order of pole (three term test) = -10.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.01 y[1] (analytic) = 3.2920860802699172062593648293701 y[1] (numeric) = 3.2920860802699172062593648293703 absolute error = 2e-31 relative error = 6.0751752877495249634525702900627e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4752 Order of pole (three term test) = -10.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4 y[1] (analytic) = 3.3072872417272238292783363661955 y[1] (numeric) = 3.3072872417272238292783363661957 absolute error = 2e-31 relative error = 6.0472521853151895944387674226035e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4767 Order of pole (three term test) = -11.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20007080, alloc=4390108, time=0.77 x[1] = -3.99 y[1] (analytic) = 3.3223576755497601333401019040203 y[1] (numeric) = 3.3223576755497601333401019040205 absolute error = 2e-31 relative error = 6.0198214500461760658984462450592e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.478 Order of pole (three term test) = -11.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.98 y[1] (analytic) = 3.3372958747067025178041274333497 y[1] (numeric) = 3.3372958747067025178041274333499 absolute error = 2e-31 relative error = 5.9928758943968956336360039941063e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4791 Order of pole (three term test) = -11.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.97 y[1] (analytic) = 3.3521003453905837462344949786387 y[1] (numeric) = 3.3521003453905837462344949786389 absolute error = 2e-31 relative error = 5.9664085019118417279235511256579e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4801 Order of pole (three term test) = -11.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.96 y[1] (analytic) = 3.366769607166672448288139617503 y[1] (numeric) = 3.3667696071666724482881396175032 absolute error = 2e-31 relative error = 5.9404124230618602342655043267800e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4808 Order of pole (three term test) = -12.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.95 y[1] (analytic) = 3.3813021931210153591603866232805 y[1] (numeric) = 3.3813021931210153591603866232806 absolute error = 1e-31 relative error = 2.9574404856046843954592025702338e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -12.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.94 y[1] (analytic) = 3.3956966500071274924872122988712 y[1] (numeric) = 3.3956966500071274924872122988713 absolute error = 1e-31 relative error = 2.9449038093491096209148427145464e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.93 y[1] (analytic) = 3.4099515383913155778091796790539 y[1] (numeric) = 3.409951538391315577809179679054 absolute error = 1e-31 relative error = 2.9325929965320318511467696692693e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.92 y[1] (analytic) = 3.4240654327966202303744051685852 y[1] (numeric) = 3.4240654327966202303744051685853 absolute error = 1e-31 relative error = 2.9205049366806220204649101186751e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.91 y[1] (analytic) = 3.4380369218453624591835272277488 y[1] (numeric) = 3.4380369218453624591835272277489 absolute error = 1e-31 relative error = 2.9086365933011886397411117951715e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -13.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.9 y[1] (analytic) = 3.4518646084002802587446609692287 y[1] (numeric) = 3.4518646084002802587446609692288 absolute error = 1e-31 relative error = 2.8969850021534778845412362295161e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -13.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.89 y[1] (analytic) = 3.4655471097042411709967766052634 y[1] (numeric) = 3.4655471097042411709967766052635 absolute error = 1e-31 relative error = 2.8855472695777106551824517790954e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -13.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.88 y[1] (analytic) = 3.4790830575185168462617361540826 y[1] (numeric) = 3.4790830575185168462617361540827 absolute error = 1e-31 relative error = 2.8743205708726534614737939116942e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4797 Order of pole (three term test) = -14.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.87 y[1] (analytic) = 3.4924710982596057758841216186546 y[1] (numeric) = 3.4924710982596057758841216186547 absolute error = 1e-31 relative error = 2.8633021487230845006952928139537e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4786 Order of pole (three term test) = -14.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.86 y[1] (analytic) = 3.5057098931345905143996092187297 y[1] (numeric) = 3.5057098931345905143996092187298 absolute error = 1e-31 relative error = 2.8524893116750781854333729379013e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4775 Order of pole (three term test) = -14.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.85 y[1] (analytic) = 3.5187981182750158556224701479056 y[1] (numeric) = 3.5187981182750158556224701479057 absolute error = 1e-31 relative error = 2.8418794326575907575984933628360e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4761 Order of pole (three term test) = -14.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.84 y[1] (analytic) = 3.5317344648692745749461538804954 y[1] (numeric) = 3.5317344648692745749461538804955 absolute error = 1e-31 relative error = 2.8314699475488866098602686370195e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4745 Order of pole (three term test) = -15.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.83 y[1] (analytic) = 3.544517639293487499393045054047 y[1] (numeric) = 3.5445176392934874993930450540471 absolute error = 1e-31 relative error = 2.8212583537863996338841440729793e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4727 Order of pole (three term test) = -15.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.82 y[1] (analytic) = 3.5571463632408648175154553133124 y[1] (numeric) = 3.5571463632408648175154553133125 absolute error = 1e-31 relative error = 2.8112422090186764289555242623877e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4708 Order of pole (three term test) = -15.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.81 y[1] (analytic) = 3.5696193738495356931246607487299 y[1] (numeric) = 3.56961937384953569312466074873 absolute error = 1e-31 relative error = 2.8014191297980986326953936334332e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4686 Order of pole (three term test) = -15.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8 y[1] (analytic) = 3.5819354238288333999931363487015 y[1] (numeric) = 3.5819354238288333999931363487015 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = -16.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.79 y[1] (analytic) = 3.5940932815840233491217545036803 y[1] (numeric) = 3.5940932815840233491217545036804 absolute error = 1e-31 relative error = 2.7823429211588809535908048689729e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4638 Order of pole (three term test) = -16.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.78 y[1] (analytic) = 3.6060917313394615358731605184754 y[1] (numeric) = 3.6060917313394615358731605184755 absolute error = 1e-31 relative error = 2.7730853081448260591099923792344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.461 Order of pole (three term test) = -16.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.77 y[1] (analytic) = 3.6179295732601710912292434923924 y[1] (numeric) = 3.6179295732601710912292434923925 absolute error = 1e-31 relative error = 2.7640117911385568135073772000287e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4582 Order of pole (three term test) = -16.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.76 y[1] (analytic) = 3.6296056235718247796188902751262 y[1] (numeric) = 3.6296056235718247796188902751263 absolute error = 1e-31 relative error = 2.7551202629444884907316082924142e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4551 Order of pole (three term test) = -16.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=24009716, alloc=4390108, time=0.92 x[1] = -3.75 y[1] (analytic) = 3.6411187146791214451662248045814 y[1] (numeric) = 3.6411187146791214451662248045815 absolute error = 1e-31 relative error = 2.7464086682164834728384455873944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4518 Order of pole (three term test) = -17.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.74 y[1] (analytic) = 3.6524676952825445688133547124051 y[1] (numeric) = 3.6524676952825445688133547124051 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4484 Order of pole (three term test) = -17.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.73 y[1] (analytic) = 3.6636514304934912605592113958433 y[1] (numeric) = 3.6636514304934912605592113958433 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4448 Order of pole (three term test) = -17.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.72 y[1] (analytic) = 3.6746688019477601740112001789793 y[1] (numeric) = 3.6746688019477601740112001789794 absolute error = 1e-31 relative error = 2.7213336871882153362773104072683e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.441 Order of pole (three term test) = -17.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.71 y[1] (analytic) = 3.6855187079173869945527783452195 y[1] (numeric) = 3.6855187079173869945527783452196 absolute error = 1e-31 relative error = 2.7133222736103814963377584601765e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.437 Order of pole (three term test) = -18.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7 y[1] (analytic) = 3.6962000634208163176713402127088 y[1] (numeric) = 3.6962000634208163176713402127089 absolute error = 1e-31 relative error = 2.7054812587024971703172639057409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4329 Order of pole (three term test) = -18.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.69 y[1] (analytic) = 3.7067118003313989003503860567443 y[1] (numeric) = 3.7067118003313989003503860567444 absolute error = 1e-31 relative error = 2.6978088771579028897672490323384e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4286 Order of pole (three term test) = -18.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.68 y[1] (analytic) = 3.7170528674842034358912497370723 y[1] (numeric) = 3.7170528674842034358912497370724 absolute error = 1e-31 relative error = 2.6903034087777869224155574042177e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4241 Order of pole (three term test) = -18.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.67 y[1] (analytic) = 3.7272222307811321710759123729596 y[1] (numeric) = 3.7272222307811321710759123729597 absolute error = 1e-31 relative error = 2.6829631776220252764878413694650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4194 Order of pole (three term test) = -18.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.66 y[1] (analytic) = 3.7372188732943298541967818403199 y[1] (numeric) = 3.7372188732943298541967818403199 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4146 Order of pole (three term test) = -19.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.65 y[1] (analytic) = 3.7470417953678756731448089490565 y[1] (numeric) = 3.7470417953678756731448089490566 absolute error = 1e-31 relative error = 2.6687719396036850787911526187058e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = -19.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.64 y[1] (analytic) = 3.7566900147177480144468744882682 y[1] (numeric) = 3.7566900147177480144468744882682 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4044 Order of pole (three term test) = -19.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.63 y[1] (analytic) = 3.766162566530052046859847088796 y[1] (numeric) = 3.766162566530052046859847088796 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3991 Order of pole (three term test) = -19.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.62 y[1] (analytic) = 3.775458503557500306844808544136 y[1] (numeric) = 3.775458503557500306844808544136 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3937 Order of pole (three term test) = -19.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.61 y[1] (analytic) = 3.7845768962141366379432993870768 y[1] (numeric) = 3.7845768962141366379432993870768 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.388 Order of pole (three term test) = -20.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.6 y[1] (analytic) = 3.7935168326682940117405834505319 y[1] (numeric) = 3.7935168326682940117405834505318 absolute error = 1e-31 relative error = 2.6360763484384418204810552982960e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3822 Order of pole (three term test) = -20.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.59 y[1] (analytic) = 3.8022774189337769347112996786957 y[1] (numeric) = 3.8022774189337769347112996786956 absolute error = 1e-31 relative error = 2.6300027321005339938446384790204e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3763 Order of pole (three term test) = -20.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.58 y[1] (analytic) = 3.810857778959259322782801709098 y[1] (numeric) = 3.810857778959259322782801709098 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3702 Order of pole (three term test) = -20.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.57 y[1] (analytic) = 3.8192570547158889039032268720735 y[1] (numeric) = 3.8192570547158889039032268720734 absolute error = 1e-31 relative error = 2.6183102778202215045598573092352e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.364 Order of pole (three term test) = -20.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.56 y[1] (analytic) = 3.8274744062830893882470412262073 y[1] (numeric) = 3.8274744062830893882470412262072 absolute error = 1e-31 relative error = 2.6126889270857675566522054916209e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3576 Order of pole (three term test) = -21.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.55 y[1] (analytic) = 3.8355090119325518259125416454209 y[1] (numeric) = 3.8355090119325518259125416454208 absolute error = 1e-31 relative error = 2.6072158790109113033915910674702e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3511 Order of pole (three term test) = -21.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.54 y[1] (analytic) = 3.8433600682104067530455377722595 y[1] (numeric) = 3.8433600682104067530455377722594 absolute error = 1e-31 relative error = 2.6018899667280783072128704691273e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3444 Order of pole (three term test) = -21.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.53 y[1] (analytic) = 3.851026790017568909243078029368 y[1] (numeric) = 3.8510267900175689092430780293679 absolute error = 1e-31 relative error = 2.5967100581905789953377763568320e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3376 Order of pole (three term test) = -21.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.52 y[1] (analytic) = 3.8585084106882464918324330245445 y[1] (numeric) = 3.8585084106882464918324330245443 absolute error = 2e-31 relative error = 5.1833501113018378700274127000487e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3307 Order of pole (three term test) = -21.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.51 y[1] (analytic) = 3.8658041820666070961653326115152 y[1] (numeric) = 3.865804182066607096165332611515 absolute error = 2e-31 relative error = 5.1735677903137525429560685752881e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3236 Order of pole (three term test) = -21.91 NO COMPLEX POLE (six term test) for Equation 1 bytes used=28010784, alloc=4455632, time=1.08 TOP MAIN SOLVE Loop x[1] = -3.5 y[1] (analytic) = 3.8729133745815926753973152533435 y[1] (numeric) = 3.8729133745815926753973152533434 absolute error = 1e-31 relative error = 2.5820355460649420243896016810803e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3164 Order of pole (three term test) = -22.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.49 y[1] (analytic) = 3.8798352773198760383185573455335 y[1] (numeric) = 3.8798352773198760383185573455334 absolute error = 1e-31 relative error = 2.5774290105707346551999801139591e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3091 Order of pole (three term test) = -22.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.48 y[1] (analytic) = 3.8865691980969515896471962947646 y[1] (numeric) = 3.8865691980969515896471962947644 absolute error = 2e-31 relative error = 5.1459266465120311055922675528656e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3016 Order of pole (three term test) = -22.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.47 y[1] (analytic) = 3.8931144635263532037703601070534 y[1] (numeric) = 3.8931144635263532037703601070532 absolute error = 2e-31 relative error = 5.1372751013038937180047136641699e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.294 Order of pole (three term test) = -22.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.46 y[1] (analytic) = 3.8994704190869923102032107515641 y[1] (numeric) = 3.8994704190869923102032107515639 absolute error = 2e-31 relative error = 5.1289015816364947792692923089323e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2863 Order of pole (three term test) = -22.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.45 y[1] (analytic) = 3.9056364291886094570135702798955 y[1] (numeric) = 3.9056364291886094570135702798953 absolute error = 2e-31 relative error = 5.1208043458758326408603938868885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2785 Order of pole (three term test) = -22.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.44 y[1] (analytic) = 3.911611877235332807110330025945 y[1] (numeric) = 3.9116118772353328071103300259448 absolute error = 2e-31 relative error = 5.1129817138544156385316278078409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2706 Order of pole (three term test) = -22.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.43 y[1] (analytic) = 3.9173961656873372115989792824511 y[1] (numeric) = 3.9173961656873372115989792824509 absolute error = 2e-31 relative error = 5.1054320661211058697363848232826e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2626 Order of pole (three term test) = -23.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.42 y[1] (analytic) = 3.9229887161205976943483002912028 y[1] (numeric) = 3.9229887161205976943483002912026 absolute error = 2e-31 relative error = 5.0981538432202756305544032456300e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2545 Order of pole (three term test) = -23.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.41 y[1] (analytic) = 3.9283889692847313724695672819059 y[1] (numeric) = 3.9283889692847313724695672819057 absolute error = 2e-31 relative error = 5.0911455449997194871794037856253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2463 Order of pole (three term test) = -23.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.4 y[1] (analytic) = 3.9335963851589220285644030795314 y[1] (numeric) = 3.9335963851589220285644030795312 absolute error = 2e-31 relative error = 5.0844057299467891206515794297204e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2379 Order of pole (three term test) = -23.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.39 y[1] (analytic) = 3.938610443005921742330672149345 y[1] (numeric) = 3.9386104430059217423306721493448 absolute error = 2e-31 relative error = 5.0779330145522416137856689157947e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2295 Order of pole (three term test) = -23.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.38 y[1] (analytic) = 3.9434306414241241814082506999811 y[1] (numeric) = 3.943430641424124181408250699981 absolute error = 1e-31 relative error = 2.5358630363506573883073746565044e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.221 Order of pole (three term test) = -23.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.37 y[1] (analytic) = 3.9480564983977043441789835319417 y[1] (numeric) = 3.9480564983977043441789835319416 absolute error = 1e-31 relative error = 2.5328918175457827302922859200056e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2124 Order of pole (three term test) = -23.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.36 y[1] (analytic) = 3.9524875513448197405883306155566 y[1] (numeric) = 3.9524875513448197405883306155565 absolute error = 1e-31 relative error = 2.5300522443385143103344514061500e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2037 Order of pole (three term test) = -23.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.35 y[1] (analytic) = 3.9567233571638681909107887505431 y[1] (numeric) = 3.9567233571638681909107887505429 absolute error = 2e-31 relative error = 5.0546874761382761760935008938320e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1949 Order of pole (three term test) = -24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.34 y[1] (analytic) = 3.9607634922777976167177598021398 y[1] (numeric) = 3.9607634922777976167177598021397 absolute error = 1e-31 relative error = 2.5247657476889877605752699982593e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1861 Order of pole (three term test) = -24.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.33 y[1] (analytic) = 3.9646075526764633931056934297185 y[1] (numeric) = 3.9646075526764633931056934297184 absolute error = 1e-31 relative error = 2.5223177495207839367674326521405e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1772 Order of pole (three term test) = -24.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.32 y[1] (analytic) = 3.9682551539570290264845791694624 y[1] (numeric) = 3.9682551539570290264845791694623 absolute error = 1e-31 relative error = 2.5199992470313532719229638317910e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1682 Order of pole (three term test) = -24.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.31 y[1] (analytic) = 3.9717059313624061178926761411711 y[1] (numeric) = 3.971705931362406117892676141171 absolute error = 1e-31 relative error = 2.5178097706165573453777950526511e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1591 Order of pole (three term test) = -24.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3 y[1] (analytic) = 3.9749595398177297678731821022057 y[1] (numeric) = 3.9749595398177297678731821022056 absolute error = 1e-31 relative error = 2.5157488773982706077697999220608e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.15 Order of pole (three term test) = -24.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.29 y[1] (analytic) = 3.978015653964865775402750251079 y[1] (numeric) = 3.9780156539648657754027502510789 absolute error = 1e-31 relative error = 2.5138161510332560851321869423148e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1408 Order of pole (three term test) = -24.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.28 y[1] (analytic) = 3.9808739681949461801807168322634 y[1] (numeric) = 3.9808739681949461801807168322634 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1316 Order of pole (three term test) = -24.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.27 y[1] (analytic) = 3.9835341966789298947519234809895 y[1] (numeric) = 3.9835341966789298947519234809895 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1223 Order of pole (three term test) = -24.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32014220, alloc=4455632, time=1.24 x[1] = -3.26 y[1] (analytic) = 3.9859960733961853704253891343433 y[1] (numeric) = 3.9859960733961853704253891343433 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.113 Order of pole (three term test) = -24.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.25 y[1] (analytic) = 3.9882593521610924387460584503432 y[1] (numeric) = 3.9882593521610924387460584503432 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1036 Order of pole (three term test) = -24.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.24 y[1] (analytic) = 3.9903238066476606683576476874849 y[1] (numeric) = 3.9903238066476606683576476874849 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09415 Order of pole (three term test) = -24.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.23 y[1] (analytic) = 3.9921892304121617754414169891699 y[1] (numeric) = 3.9921892304121617754414169891698 absolute error = 1e-31 relative error = 2.5048912821618877925424464215853e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08469 Order of pole (three term test) = -24.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.22 y[1] (analytic) = 3.9938554369137738245086854749517 y[1] (numeric) = 3.9938554369137738245086854749516 absolute error = 1e-31 relative error = 2.5038462603261964504215374304257e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07519 Order of pole (three term test) = -24.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.21 y[1] (analytic) = 3.9953222595332351551442133304085 y[1] (numeric) = 3.9953222595332351551442133304084 absolute error = 1e-31 relative error = 2.5029270107408753400167080823310e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06567 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2 y[1] (analytic) = 3.9965895515895061693233214445672 y[1] (numeric) = 3.9965895515895061693233214445671 absolute error = 1e-31 relative error = 2.5021333491758851256104861100514e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05612 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.19 y[1] (analytic) = 3.997657186354437313137901659399 y[1] (numeric) = 3.9976571863544373131379016593989 absolute error = 1e-31 relative error = 2.5014651166522980155171243704512e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04654 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.18 y[1] (analytic) = 3.9985250570654417861453683077206 y[1] (numeric) = 3.9985250570654417861453683077206 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03695 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.17 y[1] (analytic) = 3.9991930769361717110801767002706 y[1] (numeric) = 3.9991930769361717110801767002705 absolute error = 1e-31 relative error = 2.5005044286736753918217190006149e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02734 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.16 y[1] (analytic) = 3.9996611791651966963198341885479 y[1] (numeric) = 3.9996611791651966963198341885478 absolute error = 1e-31 relative error = 2.5002117809607025399701645648812e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01772 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.15 y[1] (analytic) = 3.9999293169426839232563893135895 y[1] (numeric) = 3.9999293169426839232563893135893 absolute error = 2e-31 relative error = 5.0000883553829522452788791202668e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008096 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.14 y[1] (analytic) = 3.9999974634550790905702286126901 y[1] (numeric) = 3.9999974634550790905702286126899 absolute error = 2e-31 relative error = 5.0000031706831617818546719379572e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.13 y[1] (analytic) = 3.9998656118877877473156544782784 y[1] (numeric) = 3.9998656118877877473156544782782 absolute error = 2e-31 relative error = 5.0001679907842564071740266332586e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.12 y[1] (analytic) = 3.9995337754258567466871699479512 y[1] (numeric) = 3.999533775425856746687169947951 absolute error = 2e-31 relative error = 5.0005828486522702403065175900700e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.11 y[1] (analytic) = 3.9990019872526557523216616734337 y[1] (numeric) = 3.9990019872526557523216616734335 absolute error = 2e-31 relative error = 5.0012478272710610602789265917413e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.1 y[1] (analytic) = 3.9982703005465589289847521090829 y[1] (numeric) = 3.9982703005465589289847521090828 absolute error = 1e-31 relative error = 2.5010815298387934296857728049953e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.09 y[1] (analytic) = 3.9973387884756271494694870361715 y[1] (numeric) = 3.9973387884756271494694870361714 absolute error = 1e-31 relative error = 2.5016643645092362157268007393515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.08 y[1] (analytic) = 3.9962075441902912494822370747196 y[1] (numeric) = 3.9962075441902912494822370747195 absolute error = 1e-31 relative error = 2.5023725343139536407860215962698e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.07 y[1] (analytic) = 3.9948766808140370621842273254535 y[1] (numeric) = 3.9948766808140370621842273254535 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.06 y[1] (analytic) = 3.9933463314320931638774785435863 y[1] (numeric) = 3.9933463314320931638774785435863 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.05 y[1] (analytic) = 3.9916166490781224620511644031298 y[1] (numeric) = 3.9916166490781224620511644031298 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.04 y[1] (analytic) = 3.9896878067189189566184899096864 y[1] (numeric) = 3.9896878067189189566184899096863 absolute error = 1e-31 relative error = 2.5064617795806695539274336912426e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.03 y[1] (analytic) = 3.9875599972371112046552146174169 y[1] (numeric) = 3.9875599972371112046552146174168 absolute error = 1e-31 relative error = 2.5077992574227774552125522713633e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.02 y[1] (analytic) = 3.9852334334118742182789330665261 y[1] (numeric) = 3.985233433411874218278933066526 absolute error = 1e-31 relative error = 2.5092633009049884530273995323494e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=36016460, alloc=4521156, time=1.40 x[1] = -3.01 y[1] (analytic) = 3.9827083478976517244632511483648 y[1] (numeric) = 3.9827083478976517244632511483648 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3 y[1] (analytic) = 3.9799849932008909145431455894625 y[1] (numeric) = 3.9799849932008909145431455894625 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.99 y[1] (analytic) = 3.9770636416547920099171683744217 y[1] (numeric) = 3.9770636416547920099171683744217 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.98 y[1] (analytic) = 3.9739445853920751689688839287908 y[1] (numeric) = 3.9739445853920751689688839287908 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.97 y[1] (analytic) = 3.9706281363157674584941527496123 y[1] (numeric) = 3.9706281363157674584941527496123 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.96 y[1] (analytic) = 3.9671146260680128109127746459523 y[1] (numeric) = 3.9671146260680128109127746459523 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.95 y[1] (analytic) = 3.9634044059969080862427788094039 y[1] (numeric) = 3.9634044059969080862427788094039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.94 y[1] (analytic) = 3.9594978471213685552035267626566 y[1] (numeric) = 3.9594978471213685552035267626566 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.93 y[1] (analytic) = 3.9553953400940263168700392093527 y[1] (numeric) = 3.9553953400940263168700392093526 absolute error = 1e-31 relative error = 2.5281922893103988413701550743022e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.92 y[1] (analytic) = 3.9510972951621653610058634703165 y[1] (numeric) = 3.9510972951621653610058634703165 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.91 y[1] (analytic) = 3.9466041421266971815356942132055 y[1] (numeric) = 3.9466041421266971815356942132055 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.9 y[1] (analytic) = 3.9419163302991810435622133386911 y[1] (numeric) = 3.9419163302991810435622133386911 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.89 y[1] (analytic) = 3.9370343284568932018646310144186 y[1] (numeric) = 3.9370343284568932018646310144186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.88 y[1] (analytic) = 3.931958624795949563919635809531 y[1] (numeric) = 3.9319586247959495639196358095311 absolute error = 1e-31 relative error = 2.5432617568601586367287444519065e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.87 y[1] (analytic) = 3.9266897268824864851393875174759 y[1] (numeric) = 3.9266897268824864851393875174759 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.86 y[1] (analytic) = 3.9212281616019045782063463327855 y[1] (numeric) = 3.9212281616019045782063463327856 absolute error = 1e-31 relative error = 2.5502214071406619329341812450230e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.85 y[1] (analytic) = 3.9155744751061806120817082143499 y[1] (numeric) = 3.9155744751061806120817082143499 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.84 y[1] (analytic) = 3.9097292327592527694536389871725 y[1] (numeric) = 3.9097292327592527694536389871725 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.83 y[1] (analytic) = 3.9036930190804847240540502254491 y[1] (numeric) = 3.9036930190804847240540502254491 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.82 y[1] (analytic) = 3.8974664376862141913890721275201 y[1] (numeric) = 3.8974664376862141913890721275201 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.81 y[1] (analytic) = 3.8910501112293917979794409567177 y[1] (numeric) = 3.8910501112293917979794409567177 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.8 y[1] (analytic) = 3.8844446813373163051735762347323 y[1] (numeric) = 3.8844446813373163051735762347323 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.79 y[1] (analytic) = 3.8776508085474724139590792392482 y[1] (numeric) = 3.8776508085474724139590792392482 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.78 y[1] (analytic) = 3.8706691722414775669387033382352 y[1] (numeric) = 3.8706691722414775669387033382352 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.77 y[1] (analytic) = 3.8635004705771443527355544156581 y[1] (numeric) = 3.8635004705771443527355544156582 absolute error = 1e-31 relative error = 2.5883263315627763013321982233126e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.76 y[1] (analytic) = 3.8561454204186653065304663942802 y[1] (numeric) = 3.8561454204186653065304663942803 absolute error = 1e-31 relative error = 2.5932631967272361499344115765650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=40017472, alloc=4521156, time=1.56 TOP MAIN SOLVE Loop x[1] = -2.75 y[1] (analytic) = 3.8486047572649270881933189790534 y[1] (numeric) = 3.8486047572649270881933189790535 absolute error = 1e-31 relative error = 2.5983442392007697210734012962417e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.74 y[1] (analytic) = 3.8408792351759612065307465035586 y[1] (numeric) = 3.8408792351759612065307465035586 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.73 y[1] (analytic) = 3.8329696266975386445165222497856 y[1] (numeric) = 3.8329696266975386445165222497856 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.72 y[1] (analytic) = 3.8248767227839159259792575999741 y[1] (numeric) = 3.8248767227839159259792575999742 absolute error = 1e-31 relative error = 2.6144633473890248283125458504858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.71 y[1] (analytic) = 3.8166013327187403490763691874322 y[1] (numeric) = 3.8166013327187403490763691874322 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.7 y[1] (analytic) = 3.8081442840341222959650545638867 y[1] (numeric) = 3.8081442840341222959650545638867 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.69 y[1] (analytic) = 3.7995064224278827113718697686577 y[1] (numeric) = 3.7995064224278827113718697686578 absolute error = 1e-31 relative error = 2.6319208044949177848913455032412e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.68 y[1] (analytic) = 3.7906886116789840252440916372413 y[1] (numeric) = 3.7906886116789840252440916372414 absolute error = 1e-31 relative error = 2.6380431168074150382337041622013e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.67 y[1] (analytic) = 3.7816917335611529763201257168595 y[1] (numeric) = 3.7816917335611529763201257168596 absolute error = 1e-31 relative error = 2.6443191842565059808945709079016e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.66 y[1] (analytic) = 3.7725166877547039742646220077652 y[1] (numeric) = 3.7725166877547039742646220077653 absolute error = 1e-31 relative error = 2.6507503684368641633412839992689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.65 y[1] (analytic) = 3.7631643917565718179586047321076 y[1] (numeric) = 3.7631643917565718179586047321077 absolute error = 1e-31 relative error = 2.6573380694995880412039346241472e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.64 y[1] (analytic) = 3.753635780788562766597814632532 y[1] (numeric) = 3.7536357807885627665978146325321 absolute error = 1e-31 relative error = 2.6640837268178434632068390893046e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.63 y[1] (analytic) = 3.7439318077038331384156967803899 y[1] (numeric) = 3.74393180770383313841569678039 absolute error = 1e-31 relative error = 2.6709888196743188053412604810374e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.62 y[1] (analytic) = 3.7340534428916047890932273534967 y[1] (numeric) = 3.7340534428916047890932273534968 absolute error = 1e-31 relative error = 2.6780548679710710616719026487072e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.61 y[1] (analytic) = 3.7240016741801269982283348974453 y[1] (numeric) = 3.7240016741801269982283348974454 absolute error = 1e-31 relative error = 2.6852834329623633664962233640851e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.6 y[1] (analytic) = 3.7137775067378944675954043032904 y[1] (numeric) = 3.7137775067378944675954043032905 absolute error = 1e-31 relative error = 2.6926761180111173815411995474675e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.59 y[1] (analytic) = 3.7033819629731313093127194908166 y[1] (numeric) = 3.7033819629731313093127194908167 absolute error = 1e-31 relative error = 2.7002345693696277710762006575522e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.58 y[1] (analytic) = 3.6928160824315510754352649891385 y[1] (numeric) = 3.6928160824315510754352649891385 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.57 y[1] (analytic) = 3.6820809216924030528847274431343 y[1] (numeric) = 3.6820809216924030528847274431343 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.56 y[1] (analytic) = 3.6711775542628152190005762467649 y[1] (numeric) = 3.6711775542628152190005762467649 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.55 y[1] (analytic) = 3.6601070704704444233286209516646 y[1] (numeric) = 3.6601070704704444233286209516646 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.54 y[1] (analytic) = 3.6488705773544445305394087116131 y[1] (numeric) = 3.6488705773544445305394087116132 absolute error = 1e-31 relative error = 2.7405740455860017528387610770351e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.53 y[1] (analytic) = 3.63746919855476342757131034511 y[1] (numeric) = 3.63746919855476342757131034511 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.52 y[1] (analytic) = 3.6259040741997799652053285209037 y[1] (numeric) = 3.6259040741997799652053285209037 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.51 y[1] (analytic) = 3.6141763607922920702838350157568 y[1] (numeric) = 3.6141763607922920702838350157568 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=44020108, alloc=4521156, time=1.72 TOP MAIN SOLVE Loop x[1] = -2.5 y[1] (analytic) = 3.6022872310938674296670055809347 y[1] (numeric) = 3.6022872310938674296670055809347 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.49 y[1] (analytic) = 3.5902378740075683107621826651431 y[1] (numeric) = 3.5902378740075683107621826651431 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.48 y[1] (analytic) = 3.5780294944590622460463840671807 y[1] (numeric) = 3.5780294944590622460463840671806 absolute error = 1e-31 relative error = 2.7948344236641994075594283747142e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed 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) = 3.5656633132761304704144311681231 y[1] (numeric) = 3.565663313276130470414431168123 absolute error = 1e-31 relative error = 2.8045272706390224918771925581896e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.46 y[1] (analytic) = 3.5531405670665861604085526293724 y[1] (numeric) = 3.5531405670665861604085526293723 absolute error = 1e-31 relative error = 2.8144115920119180408092772332402e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.45 y[1] (analytic) = 3.540462508094614683403806134673 y[1] (numeric) = 3.5404625080946146834038061346729 absolute error = 1e-31 relative error = 2.8244897318180446604652293665077e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.44 y[1] (analytic) = 3.5276304041555482226213501850748 y[1] (numeric) = 3.5276304041555482226213501850747 absolute error = 1e-31 relative error = 2.8347640921282459509946512959743e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed 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) = 3.5146455384490873004027104883558 y[1] (numeric) = 3.5146455384490873004027104883557 absolute error = 1e-31 relative error = 2.8452371343292599586008461085216e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.42 y[1] (analytic) = 3.5015092094509818774870651378215 y[1] (numeric) = 3.5015092094509818774870651378214 absolute error = 1e-31 relative error = 2.8559113804438478413011529330254e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed 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) = 3.4882227307831848600746887911359 y[1] (numeric) = 3.4882227307831848600746887911358 absolute error = 1e-31 relative error = 2.8667894144921112688086281775430e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed 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) = 3.4747874310824909992176444546696 y[1] (numeric) = 3.4747874310824909992176444546695 absolute error = 1e-31 relative error = 2.8778738838953171370830574372110e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed 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) = 3.4612046538676743185383165852361 y[1] (numeric) = 3.4612046538676743185383165852361 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 = 18.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.38 y[1] (analytic) = 3.4474757574051373564222952147351 y[1] (numeric) = 3.447475757405137356422295214735 absolute error = 1e-31 relative error = 2.9006730441889599025342394234058e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed 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) = 3.4336021145730856576494332176447 y[1] (numeric) = 3.4336021145730856576494332176446 absolute error = 1e-31 relative error = 2.9123933601850494247000304351270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.36 y[1] (analytic) = 3.4195851127242410969007260692902 y[1] (numeric) = 3.4195851127242410969007260692901 absolute error = 1e-31 relative error = 2.9243313648752600618415443182982e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.35 y[1] (analytic) = 3.4054261535471077626942582245178 y[1] (numeric) = 3.4054261535471077626942582245177 absolute error = 1e-31 relative error = 2.9364900453307300072071606571541e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed 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) = 3.3911266529258042750462111441227 y[1] (numeric) = 3.3911266529258042750462111441226 absolute error = 1e-31 relative error = 2.9488724614199166951819874945628e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed 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) = 3.376688040798476553508360855632 y[1] (numeric) = 3.3766880407984765535083608556319 absolute error = 1e-31 relative error = 2.9614817475514635521193097238781e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed 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) = 3.3621117610143051941872723320165 y[1] (numeric) = 3.3621117610143051941872723320164 absolute error = 1e-31 relative error = 2.9743211144721526581287764625724e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed 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) = 3.3473992711891217548883286469421 y[1] (numeric) = 3.347399271189121754888328646942 absolute error = 1e-31 relative error = 2.9873938511218068650685445764915e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed 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) = 3.332552042559648386635761142332 y[1] (numeric) = 3.332552042559648386635761142332 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed 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) = 3.3175715598363753874840620363779 y[1] (numeric) = 3.3175715598363753874840620363779 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.28 y[1] (analytic) = 3.3024593210550913907427967009214 y[1] (numeric) = 3.3024593210550913907427967009214 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed 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) = 3.2872168374270810344722686962486 y[1] (numeric) = 3.2872168374270810344722686962486 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) 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=48021748, alloc=4521156, time=1.87 x[1] = -2.26 y[1] (analytic) = 3.2718456331880050923582531374897 y[1] (numeric) = 3.2718456331880050923582531374897 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.25 y[1] (analytic) = 3.2563472454454781778267781147928 y[1] (numeric) = 3.2563472454454781778267781147928 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed 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) = 3.2407232240253592635015245326209 y[1] (numeric) = 3.2407232240253592635015245326209 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed 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) = 3.2249751313167703868238078213713 y[1] (numeric) = 3.2249751313167703868238078213713 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed 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) = 3.2091045421158590398354288750003 y[1] (numeric) = 3.2091045421158590398354288750003 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.21 y[1] (analytic) = 3.1931130434683198667552183550373 y[1] (numeric) = 3.1931130434683198667552183550373 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed 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) = 3.1770022345106914170482852253099 y[1] (numeric) = 3.1770022345106914170482852253099 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.19 y[1] (analytic) = 3.1607737263104438241804103275939 y[1] (numeric) = 3.1607737263104438241804103275939 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.18 y[1] (analytic) = 3.144429141704873401156449735325 y[1] (numeric) = 3.144429141704873401156449735325 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.17 y[1] (analytic) = 3.127970115138820263248939988833 y[1] (numeric) = 3.127970115138820263248939988833 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.16 y[1] (analytic) = 3.1113982925012252060193974879667 y[1] (numeric) = 3.1113982925012252060193974879667 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.15 y[1] (analytic) = 3.0947153309605421828083077645281 y[1] (numeric) = 3.094715330960542182808307764528 absolute error = 1e-31 relative error = 3.2313149774897666139071995704580e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.14 y[1] (analytic) = 3.0779228987990228403088998240172 y[1] (numeric) = 3.0779228987990228403088998240171 absolute error = 1e-31 relative error = 3.2489442811910291433289135609377e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.13 y[1] (analytic) = 3.0610226752458896836330524192194 y[1] (numeric) = 3.0610226752458896836330524192193 absolute error = 1e-31 relative error = 3.2668820394140685053442061193242e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.12 y[1] (analytic) = 3.0440163503094145534138037659678 y[1] (numeric) = 3.0440163503094145534138037659676 absolute error = 2e-31 relative error = 6.5702669428720590768383238480885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.11 y[1] (analytic) = 3.0269056246079192069568203141434 y[1] (numeric) = 3.0269056246079192069568203141432 absolute error = 2e-31 relative error = 6.6074078548751045753860151201031e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.1 y[1] (analytic) = 3.0096922091997149032418770474383 y[1] (numeric) = 3.0096922091997149032418770474382 absolute error = 1e-31 relative error = 3.3225988921501798271567572657832e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.09 y[1] (analytic) = 2.9923778254119979976741326237409 y[1] (numeric) = 2.9923778254119979976741326237408 absolute error = 1e-31 relative error = 3.3418239886278983530784327098394e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.08 y[1] (analytic) = 2.9749642046687186568831376995447 y[1] (numeric) = 2.9749642046687186568831376995446 absolute error = 1e-31 relative error = 3.3613849821475630600465308443733e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.07 y[1] (analytic) = 2.9574530883174399065546542780235 y[1] (numeric) = 2.9574530883174399065546542780234 absolute error = 1e-31 relative error = 3.3812877842431711707122279559445e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.06 y[1] (analytic) = 2.9398462274552043262462192529758 y[1] (numeric) = 2.9398462274552043262462192529757 absolute error = 1e-31 relative error = 3.4015384568791614482411895864399e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.05 y[1] (analytic) = 2.9221453827534258043718599883348 y[1] (numeric) = 2.9221453827534258043718599883347 absolute error = 1e-31 relative error = 3.4221432167681481202329698407370e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.04 y[1] (analytic) = 2.9043523242818238640345404105827 y[1] (numeric) = 2.9043523242818238640345404105826 absolute error = 1e-31 relative error = 3.4431084398387369600668011908329e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.03 y[1] (analytic) = 2.8864688313314181661270334633922 y[1] (numeric) = 2.8864688313314181661270334633921 absolute error = 1e-31 relative error = 3.4644406658593229160231955709862e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.02 y[1] (analytic) = 2.8684966922366008901034057481804 y[1] (numeric) = 2.8684966922366008901034057481803 absolute error = 1e-31 relative error = 3.4861466032240327961466686513681e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=52022724, alloc=4521156, time=2.03 x[1] = -2.01 y[1] (analytic) = 2.8504377041963047850347646803309 y[1] (numeric) = 2.8504377041963047850347646803308 absolute error = 1e-31 relative error = 3.5082331339072537923447625470108e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 2.8322936730942847739951364590015 y[1] (numeric) = 2.8322936730942847739951364590015 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 2.8140664133185310834672714322606 y[1] (numeric) = 2.8140664133185310834672714322606 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 2.7957577475798319563049477198144 y[1] (numeric) = 2.7957577475798319563049477198144 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 2.7773695067295040918292796277586 y[1] (numeric) = 2.7773695067295040918292796277586 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 2.7589035295763090398631304308949 y[1] (numeric) = 2.7589035295763090398631304308949 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 2.7403616627025738569116569182614 y[1] (numeric) = 2.7403616627025738569116569182614 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 2.7217457602795344122701353716815 y[1] (numeric) = 2.7217457602795344122701353716815 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 2.7030576838819198095745781294237 y[1] (numeric) = 2.7030576838819198095745781294238 absolute error = 1e-31 relative error = 3.6995140945859442224061099509459e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 2.6842993023017964651984732063181 y[1] (numeric) = 2.6842993023017964651984732063181 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 2.6654724913616904589326778787951 y[1] (numeric) = 2.6654724913616904589326778787951 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 2.6465791337270068445576673901606 y[1] (numeric) = 2.6465791337270068445576673901607 absolute error = 1e-31 relative error = 3.7784624961950955967737981189767e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 2.6276211187177646782207648311025 y[1] (numeric) = 2.6276211187177646782207648311025 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 2.6086003421196665909586275190445 y[1] (numeric) = 2.6086003421196665909586275190445 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 2.5895187059945217982502961296198 y[1] (numeric) = 2.5895187059945217982502961296198 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 2.5703781184900415041418709765782 y[1] (numeric) = 2.5703781184900415041418709765783 absolute error = 1e-31 relative error = 3.8904781860944492439283745360753e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 2.5511804936490257202438996709496 y[1] (numeric) = 2.5511804936490257202438996709497 absolute error = 1e-31 relative error = 3.9197540216751644874321928449834e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 2.5319277512179605807605659665632 y[1] (numeric) = 2.5319277512179605807605659665633 absolute error = 1e-31 relative error = 3.9495597752303918950340591298270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 2.5126218164550452936596751672371 y[1] (numeric) = 2.5126218164550452936596751672372 absolute error = 1e-31 relative error = 3.9799065400572651319133416450721e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 2.4932646199376679251283420896617 y[1] (numeric) = 2.4932646199376679251283420896619 absolute error = 2e-31 relative error = 8.0216114407062029721151085526849e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 2.473858097369349269575499701684 y[1] (numeric) = 2.4738580973693492695754997016841 absolute error = 1e-31 relative error = 4.0422690414756602274521284258620e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 2.4544041893861741106333486130612 y[1] (numeric) = 2.4544041893861741106333486130613 absolute error = 1e-31 relative error = 4.0743085606046476296829126148877e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 2.4349048413627292298703405289292 y[1] (numeric) = 2.4349048413627292298703405289294 absolute error = 2e-31 relative error = 8.2138733556448615412048579907676e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 2.4153620032175675692531065806253 y[1] (numeric) = 2.4153620032175675692531065806254 absolute error = 1e-31 relative error = 4.1401661476328333691003774735024e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 2.3957776292182180007789716834608 y[1] (numeric) = 2.3957776292182180007789716834609 absolute error = 1e-31 relative error = 4.1740100909378496674844310660940e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 2.3761536777857602021396003530082 y[1] (numeric) = 2.3761536777857602021396003530083 absolute error = 1e-31 relative error = 4.2084820074931299685846569545754e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 bytes used=56024052, alloc=4521156, time=2.18 NO POLE (ratio test) for Equation 1 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) = 2.3564921112989841807653538878853 y[1] (numeric) = 2.3564921112989841807653538878854 absolute error = 1e-31 relative error = 4.2435957888641673409646909106746e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 2.3367948958981540301347546306902 y[1] (numeric) = 2.3367948958981540301347546306903 absolute error = 1e-31 relative error = 4.2793657319062529111986249083347e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 2.3170640012883955418098967026851 y[1] (numeric) = 2.3170640012883955418098967026853 absolute error = 2e-31 relative error = 8.6316131055849420456821578853812e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 2.2973014005427273342727565606624 y[1] (numeric) = 2.2973014005427273342727565606625 absolute error = 1e-31 relative error = 4.3529334016152795879001757767515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 2.2775090699047551952853795661022 y[1] (numeric) = 2.2775090699047551952853795661023 absolute error = 1e-31 relative error = 4.3907618775885697164662986274691e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 2.2576889885910493681752857146697 y[1] (numeric) = 2.2576889885910493681752857146698 absolute error = 1e-31 relative error = 4.4293080448785270323605956900799e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 2.2378431385932245441527809396662 y[1] (numeric) = 2.2378431385932245441527809396662 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 2.2179735044797423524960094683456 y[1] (numeric) = 2.2179735044797423524960094683457 absolute error = 1e-31 relative error = 4.5086201344617252786543916193572e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 2.1980820731974561681895646848972 y[1] (numeric) = 2.1980820731974561681895646848973 absolute error = 1e-31 relative error = 4.5494206617378152961492340403267e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 2.1781708338729180823705158633012 y[1] (numeric) = 2.1781708338729180823705158633013 absolute error = 1e-31 relative error = 4.5910081268600046439763848973193e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 2.1582417776134679047192291946826 y[1] (numeric) = 2.1582417776134679047192291946826 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 2.1382968973081240887289854149132 y[1] (numeric) = 2.1382968973081240887289854149133 absolute error = 1e-31 relative error = 4.6766190478922165398136456161881e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 2.1183381874282964905959433948396 y[1] (numeric) = 2.1183381874282964905959433948397 absolute error = 1e-31 relative error = 4.7206815509190217220591358450533e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 2.0983676438283408902874885494247 y[1] (numeric) = 2.0983676438283408902874885494248 absolute error = 1e-31 relative error = 4.7656091292732782055654246581825e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 2.078387263545975219170655219202 y[1] (numeric) = 2.0783872635459752191706552192022 absolute error = 2e-31 relative error = 9.6228457279311977262859895891363e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 2.058399044602577452411540925893 y[1] (numeric) = 2.0583990446025774524115409258932 absolute error = 2e-31 relative error = 9.7162890025833024657822769616757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 2.0384049858033851361900546924868 y[1] (numeric) = 2.038404985803385136190054692487 absolute error = 2e-31 relative error = 9.8115929559098444104692907050142e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 2.0184070865376165296107781139655 y[1] (numeric) = 2.0184070865376165296107781139656 absolute error = 1e-31 relative error = 4.9544019473068930846946040521527e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 1.9984073465785333490291829327093 y[1] (numeric) = 1.9984073465785333490291829327094 absolute error = 1e-31 relative error = 5.0039848067617281022809994434768e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0007679 Order of pole (three term test) = -0.8929 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 1.9784077658834651083521586724782 y[1] (numeric) = 1.9784077658834651083521586724783 absolute error = 1e-31 relative error = 5.0545697264458846323583578900401e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01041 Order of pole (three term test) = -0.8957 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 1.9584103443938150527121744506089 y[1] (numeric) = 1.958410344393815052712174450609 absolute error = 1e-31 relative error = 5.1061821791465724590563267384745e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02005 Order of pole (three term test) = -0.9033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 1.9384170818350676847550463858472 y[1] (numeric) = 1.9384170818350676847550463858473 absolute error = 1e-31 relative error = 5.1588484716267377705781527230635e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02968 Order of pole (three term test) = -0.9158 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 1.9184299775168178826220219858478 y[1] (numeric) = 1.9184299775168178826220219858479 absolute error = 1e-31 relative error = 5.2125957773782416700481346003982e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0393 Order of pole (three term test) = -0.9331 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 1.8984510301328416065477414596946 y[1] (numeric) = 1.8984510301328416065477414596947 absolute error = 1e-31 relative error = 5.2674521708891607234165505446590e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0489 Order of pole (three term test) = -0.9552 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 1.8784822375612281868368089701676 y[1] (numeric) = 1.8784822375612281868368089701678 bytes used=60025368, alloc=4521156, time=2.34 absolute error = 2e-31 relative error = 1.0646893327011355371488932734048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05848 Order of pole (three term test) = -0.9821 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 1.8585255966645941798236202971315 y[1] (numeric) = 1.8585255966645941798236202971316 absolute error = 1e-31 relative error = 5.3806092409738748707249848863757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06804 Order of pole (three term test) = -1.014 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 1.8385831030903987702633630308726 y[1] (numeric) = 1.8385831030903987702633630308727 absolute error = 1e-31 relative error = 5.4389709027519131502064139084487e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07757 Order of pole (three term test) = -1.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 1.8186567510713806884475469187043 y[1] (numeric) = 1.8186567510713806884475469187045 absolute error = 2e-31 relative error = 1.0997127406377201232948552864748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08707 Order of pole (three term test) = -1.092 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 1.7987485332261365981860507970752 y[1] (numeric) = 1.7987485332261365981860507970754 absolute error = 2e-31 relative error = 1.1118841589340505656560808239990e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09654 Order of pole (three term test) = -1.138 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 1.7788604403598608976507037817533 y[1] (numeric) = 1.7788604403598608976507037817535 absolute error = 2e-31 relative error = 1.1243152945688099561391407450166e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.106 Order of pole (three term test) = -1.188 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 1.758994461265266858934266745504 y[1] (numeric) = 1.7589944612652668589342667455042 absolute error = 2e-31 relative error = 1.1370132448065668286282929550296e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1154 Order of pole (three term test) = -1.244 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 1.7391525825237090140449596877417 y[1] (numeric) = 1.7391525825237090140449596877419 absolute error = 2e-31 relative error = 1.1499853549927008667550192381032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1247 Order of pole (three term test) = -1.304 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (analytic) = 1.7193367883065266749322047508502 y[1] (numeric) = 1.7193367883065266749322047508504 absolute error = 2e-31 relative error = 1.1632392289877741783000085837894e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.134 Order of pole (three term test) = -1.369 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (analytic) = 1.6995490601766284530260357940482 y[1] (numeric) = 1.6995490601766284530260357940484 absolute error = 2e-31 relative error = 1.1767827401182209385971942024681e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1432 Order of pole (three term test) = -1.438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (analytic) = 1.6797913768903376196728749012782 y[1] (numeric) = 1.6797913768903376196728749012784 absolute error = 2e-31 relative error = 1.1906240426727507046812268586386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1524 Order of pole (three term test) = -1.513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 1.6600657141995181227665039295927 y[1] (numeric) = 1.6600657141995181227665039295929 absolute error = 2e-31 relative error = 1.2047715839757571399385756415498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1615 Order of pole (three term test) = -1.591 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.39 y[1] (analytic) = 1.6403740446540010468076735643919 y[1] (numeric) = 1.6403740446540010468076735643921 absolute error = 2e-31 relative error = 1.2192341170710572467043369891108e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1706 Order of pole (three term test) = -1.675 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.38 y[1] (analytic) = 1.6207183374043312735816998528036 y[1] (numeric) = 1.6207183374043312735816998528038 absolute error = 2e-31 relative error = 1.2340207140514674346288780941448e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1795 Order of pole (three term test) = -1.762 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.37 y[1] (analytic) = 1.6011005580048540686236032207094 y[1] (numeric) = 1.6011005580048540686236032207096 absolute error = 2e-31 relative error = 1.2491407800720637716078973123310e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1885 Order of pole (three term test) = -1.855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36 y[1] (analytic) = 1.5815226682171612846480494952163 y[1] (numeric) = 1.5815226682171612846480494952165 absolute error = 2e-31 relative error = 1.2646040680874875427349687237699e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1973 Order of pole (three term test) = -1.951 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.35 y[1] (analytic) = 1.5619866258139168371599556539787 y[1] (numeric) = 1.561986625813916837159955653979 absolute error = 3e-31 relative error = 1.9206310415345368641187810010832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.206 Order of pole (three term test) = -2.052 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.34 y[1] (analytic) = 1.5424943843830810695347210153997 y[1] (numeric) = 1.5424943843830810695347210154 absolute error = 3e-31 relative error = 1.9449017321381346204710667555095e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2147 Order of pole (three term test) = -2.158 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (analytic) = 1.5230478931325535849684300279788 y[1] (numeric) = 1.5230478931325535849684300279791 absolute error = 3e-31 relative error = 1.9697345129638051565004877458097e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2233 Order of pole (three term test) = -2.268 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.32 y[1] (analytic) = 1.5036490966952540808520345411453 y[1] (numeric) = 1.5036490966952540808520345411455 absolute error = 2e-31 relative error = 1.3300975635842394979810562118441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2318 Order of pole (three term test) = -2.382 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.31 y[1] (analytic) = 1.4842999349346606773236460427676 y[1] (numeric) = 1.4842999349346606773236460427678 absolute error = 2e-31 relative error = 1.3474365611206744358261933616895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2402 Order of pole (three term test) = -2.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (analytic) = 1.4650023427508251860040317814143 y[1] (numeric) = 1.4650023427508251860040317814144 absolute error = 1e-31 relative error = 6.8259276508889851330157218437498e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2485 Order of pole (three term test) = -2.623 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.29 y[1] (analytic) = 1.4457582498868847172267878198776 y[1] (numeric) = 1.4457582498868847172267878198778 absolute error = 2e-31 relative error = 1.3833571415943701751297561008642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2567 Order of pole (three term test) = -2.749 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.28 y[1] (analytic) = 1.4265695807360889744412262128148 y[1] (numeric) = 1.426569580736088974441226212815 absolute error = 2e-31 relative error = 1.4019645638090988467753668089730e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2648 Order of pole (three term test) = -2.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27 y[1] (analytic) = 1.4074382541493625328977259678241 y[1] (numeric) = 1.4074382541493625328977259678243 absolute error = 2e-31 relative error = 1.4210214864514778432912451482654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2728 Order of pole (three term test) = -3.015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=64026588, alloc=4521156, time=2.50 x[1] = -1.26 y[1] (analytic) = 1.388366183243421346227315021647 y[1] (numeric) = 1.3883661832434213462273150216472 absolute error = 2e-31 relative error = 1.4405421452485358408549029259662e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2807 Order of pole (three term test) = -3.154 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.25 y[1] (analytic) = 1.3693552752094626691049228951239 y[1] (numeric) = 1.3693552752094626691049228951241 absolute error = 2e-31 relative error = 1.4605413483320251647917090647585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2885 Order of pole (three term test) = -3.296 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.24 y[1] (analytic) = 1.3504074311224475268446131686052 y[1] (numeric) = 1.3504074311224475268446131686054 absolute error = 2e-31 relative error = 1.4810345040367679876971585634013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2962 Order of pole (three term test) = -3.443 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.23 y[1] (analytic) = 1.3315245457509948035209055090047 y[1] (numeric) = 1.3315245457509948035209055090048 absolute error = 1e-31 relative error = 7.5101882514376688788012953675962e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3037 Order of pole (three term test) = -3.593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.22 y[1] (analytic) = 1.3127085073679059590489540511296 y[1] (numeric) = 1.3127085073679059590489540511297 absolute error = 1e-31 relative error = 7.6178374283951770071276414522781e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3111 Order of pole (three term test) = -3.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.21 y[1] (analytic) = 1.2939611975613393225939785726704 y[1] (numeric) = 1.2939611975613393225939785726705 absolute error = 1e-31 relative error = 7.7282070118072122615019220736677e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3184 Order of pole (three term test) = -3.905 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (analytic) = 1.2752844910466528447232532887538 y[1] (numeric) = 1.2752844910466528447232532887539 absolute error = 1e-31 relative error = 7.8413876042613749324452115264341e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3256 Order of pole (three term test) = -4.067 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.19 y[1] (analytic) = 1.2566802554789341238686408832991 y[1] (numeric) = 1.2566802554789341238686408832991 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3327 Order of pole (three term test) = -4.232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18 y[1] (analytic) = 1.2381503512662364539408010665745 y[1] (numeric) = 1.2381503512662364539408010665745 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3396 Order of pole (three term test) = -4.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.17 y[1] (analytic) = 1.219696631383539569334676129899 y[1] (numeric) = 1.219696631383539569334676129899 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3463 Order of pole (three term test) = -4.572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.16 y[1] (analytic) = 1.201320941187453691096720753212 y[1] (numeric) = 1.201320941187453691096720753212 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.353 Order of pole (three term test) = -4.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.15 y[1] (analytic) = 1.1830251182316854036948465623802 y[1] (numeric) = 1.1830251182316854036948465623802 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3595 Order of pole (three term test) = -4.926 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.14 y[1] (analytic) = 1.1648109920832838156496265183548 y[1] (numeric) = 1.1648109920832838156496265183549 absolute error = 1e-31 relative error = 8.5850838187188067520444821235886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3658 Order of pole (three term test) = -5.108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.13 y[1] (analytic) = 1.1466803841396853792575683286929 y[1] (numeric) = 1.146680384139685379257568328693 absolute error = 1e-31 relative error = 8.7208259060807550413890072911428e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.372 Order of pole (three term test) = -5.293 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.12 y[1] (analytic) = 1.1286351074465756647720224120777 y[1] (numeric) = 1.1286351074465756647720224120778 absolute error = 1e-31 relative error = 8.8602595595524246767385107136981e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3781 Order of pole (three term test) = -5.481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.11 y[1] (analytic) = 1.1106769665165863027125249761329 y[1] (numeric) = 1.1106769665165863027125249761329 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.384 Order of pole (three term test) = -5.672 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (analytic) = 1.0928077571488452244572598964306 y[1] (numeric) = 1.0928077571488452244572598964306 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3897 Order of pole (three term test) = -5.866 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09 y[1] (analytic) = 1.0750292662493982459442058522497 y[1] (numeric) = 1.0750292662493982459442058522497 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3953 Order of pole (three term test) = -6.063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.08 y[1] (analytic) = 1.0573432716525199521729504229479 y[1] (numeric) = 1.0573432716525199521729504229479 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4007 Order of pole (three term test) = -6.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.07 y[1] (analytic) = 1.0397515419429317512698138636482 y[1] (numeric) = 1.0397515419429317512698138636481 absolute error = 1e-31 relative error = 9.6176822987090739853220028140128e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.406 Order of pole (three term test) = -6.464 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.06 y[1] (analytic) = 1.0222558362789448761627249200872 y[1] (numeric) = 1.0222558362789448761627249200871 absolute error = 1e-31 relative error = 9.7822870216133265079915273219518e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4111 Order of pole (three term test) = -6.669 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.05 y[1] (analytic) = 1.0048579042165460194183008543758 y[1] (numeric) = 1.0048579042165460194183008543757 absolute error = 1e-31 relative error = 9.9516558092824719900684299305615e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.416 Order of pole (three term test) = -6.877 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.04 y[1] (analytic) = 0.9875594855344431925310531580157 y[1] (numeric) = 0.98755948553444319253105315801555 absolute error = 1.5e-31 relative error = 1.5188958457406102024124999860818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4208 Order of pole (three term test) = -7.086 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.03 y[1] (analytic) = 0.9703623100600893049329954003253 y[1] (numeric) = 0.9703623100600893049329954003252 absolute error = 1.0e-31 relative error = 1.0305429112741151217609769623687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4254 Order of pole (three term test) = -7.298 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02 y[1] (analytic) = 0.9532680974967008602207723839324 y[1] (numeric) = 0.95326809749670086022077238393228 absolute error = 1.2e-31 relative error = 1.2588273992922049377071349637787e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4299 Order of pole (three term test) = -7.513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=68031764, alloc=4521156, time=2.65 x[1] = -1.01 y[1] (analytic) = 0.9362785572512890675865372884416 y[1] (numeric) = 0.93627855725128906758653728844154 absolute error = 6e-32 relative error = 6.4083492605178310086573930906761e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4341 Order of pole (three term test) = -7.729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.919395388263720565198126785114 y[1] (numeric) = 0.91939538826372056519812678511394 absolute error = 6e-32 relative error = 6.5260279490100642323303602789685e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4382 Order of pole (three term test) = -7.948 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.9026202788368248493137471826928 y[1] (numeric) = 0.90262027883682484931374718269267 absolute error = 1.3e-31 relative error = 1.4402512667622142106558973151563e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -8.169 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.8859549064675653982466834652801 y[1] (numeric) = 0.88595490646756539824668346528002 absolute error = 8e-32 relative error = 9.0298049501155712911751054599910e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4459 Order of pole (three term test) = -8.391 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.8694009376792913739269444903003 y[1] (numeric) = 0.86940093767929137392694449030018 absolute error = 1.2e-31 relative error = 1.3802607611663993078602196456530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -8.616 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 0.8529600278550866757498983992963 y[1] (numeric) = 0.85296002785508667574989839929619 absolute error = 1.1e-31 relative error = 1.2896266695710670368355534157628e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4528 Order of pole (three term test) = -8.842 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.8366338210722330116676380524791 y[1] (numeric) = 0.83663382107223301166763805247899 absolute error = 1.1e-31 relative error = 1.3147926515691607058025927476455e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.456 Order of pole (three term test) = -9.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = 0.820423949937803540078020369552 y[1] (numeric) = 0.82042394993780354007802036955187 absolute error = 1.3e-31 relative error = 1.5845466238504534034931852707701e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -9.299 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = 0.804332035425403523010185831134 y[1] (numeric) = 0.80433203542540352301018583113393 absolute error = 7e-32 relative error = 8.7028735543248217506070648305582e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -9.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = 0.7883596867130743164051905866512 y[1] (numeric) = 0.78835968671307431640519058665115 absolute error = 5e-32 relative error = 6.3422826969331878056431954095549e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4645 Order of pole (three term test) = -9.762 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 0.7725085010223769069576435476506 y[1] (numeric) = 0.77250850102237690695764354765054 absolute error = 6e-32 relative error = 7.7669048198942741388632985563331e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -9.995 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 0.7567800634586710870305676971857 y[1] (numeric) = 0.75678006345867108703056769718563 absolute error = 7e-32 relative error = 9.2497151259617989017398536914670e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -10.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = 0.7411759468526062395928938852395 y[1] (numeric) = 0.74117594685260623959289388523939 absolute error = 1.1e-31 relative error = 1.4841280328525707158272656691238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -10.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = 0.7256977116028395839690027885558 y[1] (numeric) = 0.72569771160283958396900278855571 absolute error = 9e-32 relative error = 1.2401858041031727958835743389155e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -10.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 0.7103469055199976104446723890343 y[1] (numeric) = 0.71034690551999761044467238903424 absolute error = 6e-32 relative error = 8.4465772334262511106203491288066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -10.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = 0.6951250636718963074559386715523 y[1] (numeric) = 0.69512506367189630745593867155218 absolute error = 1.2e-31 relative error = 1.7263080598204527536582465424132e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -11.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = 0.6800337082300356592091679410771 y[1] (numeric) = 0.68003370823003565920916794107696 absolute error = 1.4e-31 relative error = 2.0587214766807127860545415333172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4778 Order of pole (three term test) = -11.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = 0.6650743483173837641546579262583 y[1] (numeric) = 0.66507434831738376415465792625818 absolute error = 1.2e-31 relative error = 1.8043095528130960817450923596830e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -11.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = 0.6502484798574657957750741642711 y[1] (numeric) = 0.65024847985746579577507416427099 absolute error = 1.1e-31 relative error = 1.6916610097129631980651023502541e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -11.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 0.6355575854247728966668840431261 y[1] (numeric) = 0.63555758542477289666688404312604 absolute error = 6e-32 relative error = 9.4405292889233931931997180235529e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -12.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = 0.6210031340965059649007215186398 y[1] (numeric) = 0.6210031340965059649007215186397 absolute error = 1.0e-31 relative error = 1.6102978311935486206791468653127e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 0.6065865813056691581585000367154 y[1] (numeric) = 0.60658658130566915815850003671526 absolute error = 1.4e-31 relative error = 2.3079969836894834061013925844631e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 0.5923093686955278061744382778301 y[1] (numeric) = 0.59230936869552780617443827783001 absolute error = 9e-32 relative error = 1.5194762189598899588780390859207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = 0.5781729239754452855674699524709 y[1] (numeric) = 0.57817292397544528556746995247079 absolute error = 1.1e-31 relative error = 1.9025449902367210279987157478748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 0.5641786607781132732574188693513 y[1] (numeric) = 0.56417866077811327325741886935123 absolute error = 7e-32 relative error = 1.2407417165239153173367949433388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=72034488, alloc=4521156, time=2.81 x[1] = -0.76 y[1] (analytic) = 0.550327978518189655320623266666 y[1] (numeric) = 0.5503279785181896553206232666659 absolute error = 1.0e-31 relative error = 1.8170982378409961385780431705115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -13.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = 0.5366222622523582273763224939998 y[1] (numeric) = 0.53662226225235822737632249399974 absolute error = 6e-32 relative error = 1.1181049356424892793965828082818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -13.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = 0.5230628825408241804171508786023 y[1] (numeric) = 0.52306288254082418041715087860225 absolute error = 5e-32 relative error = 9.5590801161651121148243125131636e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -14.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = 0.5096511953102592224197356828993 y[1] (numeric) = 0.50965119531025922241973568289924 absolute error = 6e-32 relative error = 1.1772757633477918894904451788035e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -14.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = 0.4963885417182100411090260754961 y[1] (numeric) = 0.49638854171821004110902607549601 absolute error = 9e-32 relative error = 1.8130958399739053650671143613172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4777 Order of pole (three term test) = -14.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = 0.4832762480189836669170841117209 y[1] (numeric) = 0.4832762480189836669170841117208 absolute error = 1.0e-31 relative error = 2.0692099065475256055881542758270e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -14.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = 0.4703156254310231474882800196163 y[1] (numeric) = 0.47031562543102314748828001961618 absolute error = 1.2e-31 relative error = 2.5514780609303675493037244369476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -15.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.69 y[1] (analytic) = 0.4575079700057867960529213690045 y[1] (numeric) = 0.45750797000578679605292136900438 absolute error = 1.2e-31 relative error = 2.6229051266250548224680302491422e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -15.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.68 y[1] (analytic) = 0.4448545624981441256352118319114 y[1] (numeric) = 0.44485456249814412563521183191128 absolute error = 1.2e-31 relative error = 2.6975108297445105807983284375358e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -15.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = 0.4323566682383014293941157103238 y[1] (numeric) = 0.43235666823830142939411571032368 absolute error = 1.2e-31 relative error = 2.7754862782377572875369371904382e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.469 Order of pole (three term test) = -15.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = 0.4200155370052698144323658175395 y[1] (numeric) = 0.42001553700526981443236581753943 absolute error = 7e-32 relative error = 1.6666050141645529194871245947658e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4667 Order of pole (three term test) = -15.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = 0.4078324029018883421647908586402 y[1] (numeric) = 0.40783240290188834216479085864011 absolute error = 9e-32 relative error = 2.2067888514893499345413151532873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4642 Order of pole (three term test) = -16.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (analytic) = 0.3958084842314147728277784414794 y[1] (numeric) = 0.39580848423141477282777844147927 absolute error = 1.3e-31 relative error = 3.2844167110878236074693438901327e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -16.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.63 y[1] (analytic) = 0.3839449833756962549525820684459 y[1] (numeric) = 0.38394498337569625495258206844581 absolute error = 9e-32 relative error = 2.3440858429431170025704033386603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -16.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = 0.3722430866749321426320006912786 y[1] (numeric) = 0.37224308667493214263200069127853 absolute error = 7e-32 relative error = 1.8804916063123218652612714675184e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4556 Order of pole (three term test) = -16.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = 0.3607039643090409641985068426904 y[1] (numeric) = 0.36070396430904096419850684269028 absolute error = 1.2e-31 relative error = 3.3268278664436133239495099942435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4524 Order of pole (three term test) = -17.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = 0.3493287701806434055180950020892 y[1] (numeric) = 0.34932877018064340551809500208917 absolute error = 3e-32 relative error = 8.5878984386217395715899328797487e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.449 Order of pole (three term test) = -17.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (analytic) = 0.3381186417996730095040069550186 y[1] (numeric) = 0.33811864179967300950400695501856 absolute error = 4e-32 relative error = 1.1830167005018024865899752349615e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4454 Order of pole (three term test) = -17.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = 0.3270747001696261306842253439 y[1] (numeric) = 0.32707470016962613068422534389988 absolute error = 1.2e-31 relative error = 3.6688866469270198953411804550964e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4416 Order of pole (three term test) = -17.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (analytic) = 0.316198049675462519732487272168 y[1] (numeric) = 0.31619804967546251973248727216789 absolute error = 1.1e-31 relative error = 3.4788323366605565113793730026194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4377 Order of pole (three term test) = -18.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = 0.3054897779731677478109489922674 y[1] (numeric) = 0.30548977797316774781094899226728 absolute error = 1.2e-31 relative error = 3.9281183415092869718469400940943e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -18.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = 0.2949509558809885143900364047645 y[1] (numeric) = 0.29495095588098851439003640476437 absolute error = 1.3e-31 relative error = 4.4075124154693182293308540874674e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4293 Order of pole (three term test) = -18.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = 0.2845826372723517149240624421644 y[1] (numeric) = 0.28458263727235171492406244216432 absolute error = 8e-32 relative error = 2.8111342549488806823548260918642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4248 Order of pole (three term test) = -18.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.53 y[1] (analytic) = 0.2743858589704779763866099628716 y[1] (numeric) = 0.27438585897047797638660996287151 absolute error = 9e-32 relative error = 3.2800524173398957302601570098463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4202 Order of pole (three term test) = -18.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = 0.264361640644700199224304856023 y[1] (numeric) = 0.26436164064470019922430485602289 absolute error = 1.1e-31 relative error = 4.1609667624902913268990099902670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4154 Order of pole (three term test) = -19.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.51 y[1] (analytic) = 0.254510984708497473788383052849 y[1] (numeric) = 0.2545109847084974737883830528489 absolute error = 1.0e-31 relative error = 3.9291034968307697802240923805290e-29 % Correct digits = 31 h = 0.01 bytes used=76035140, alloc=4586680, time=2.97 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4104 Order of pole (three term test) = -19.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (analytic) = 0.2448348762192545677674368347923 y[1] (numeric) = 0.24483487621925456776743683479226 absolute error = 4e-32 relative error = 1.6337541700627321395365592147389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4053 Order of pole (three term test) = -19.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (analytic) = 0.2353342827797570085890636817267 y[1] (numeric) = 0.2353342827797570085890636817266 absolute error = 1.0e-31 relative error = 4.2492746411107172102283847733567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4 Order of pole (three term test) = -19.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (analytic) = 0.2260101544414316112000903376825 y[1] (numeric) = 0.22601015444143161120009033768243 absolute error = 7e-32 relative error = 3.0972059716962777596955697711048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3945 Order of pole (three term test) = -19.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (analytic) = 0.2168634236093421270919614469332 y[1] (numeric) = 0.21686342360934212709196144693313 absolute error = 7e-32 relative error = 3.2278380021380660669038855020917e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3889 Order of pole (three term test) = -20.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (analytic) = 0.2078950049489495149272201929992 y[1] (numeric) = 0.2078950049489495149272201929991 absolute error = 1.0e-31 relative error = 4.8101203790132378534399575722065e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3832 Order of pole (three term test) = -20.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = 0.1991057952946461566623187770271 y[1] (numeric) = 0.19910579529464615666231877702702 absolute error = 8e-32 relative error = 4.0179644134221318268471330804715e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3773 Order of pole (three term test) = -20.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (analytic) = 0.1904966735600731656689252220033 y[1] (numeric) = 0.19049667356007316566892522200317 absolute error = 1.3e-31 relative error = 6.8242661444166621068982618367850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3712 Order of pole (three term test) = -20.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = 0.1820685006502297550481790446731 y[1] (numeric) = 0.18206850065022975504817904467302 absolute error = 8e-32 relative error = 4.3939506127799293637192063319412e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.365 Order of pole (three term test) = -20.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (analytic) = 0.1738221193753834551278224206687 y[1] (numeric) = 0.17382211937538345512782242066858 absolute error = 1.2e-31 relative error = 6.9036093007731616010457240758315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3586 Order of pole (three term test) = -21.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = 0.165758354366789789048715883446 y[1] (numeric) = 0.16575835436678978904871588344588 absolute error = 1.2e-31 relative error = 7.2394541112820301877213695380697e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3521 Order of pole (three term test) = -21.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (analytic) = 0.1578780119942298344029465358964 y[1] (numeric) = 0.15787801199422983440294653589631 absolute error = 9e-32 relative error = 5.7006038309685165538307241611507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3455 Order of pole (three term test) = -21.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = 0.1501818802853739170986464942378 y[1] (numeric) = 0.15018188028537391709864649423771 absolute error = 9e-32 relative error = 5.9927335993518668072625469029424e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3387 Order of pole (three term test) = -21.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = 0.1426707288469795010149383845509 y[1] (numeric) = 0.1426707288469795010149383845508 absolute error = 1.0e-31 relative error = 7.0091462213846475281943636390537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3318 Order of pole (three term test) = -21.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (analytic) = 0.1353453087879311535923741910182 y[1] (numeric) = 0.13534530878793115359237419101816 absolute error = 4e-32 relative error = 2.9554035051687606846439935225585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3247 Order of pole (three term test) = -21.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = 0.1282063526441302832981752637505 y[1] (numeric) = 0.12820635264413028329817526375043 absolute error = 7e-32 relative error = 5.4599478540898054875773198227703e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3175 Order of pole (three term test) = -22.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = 0.1212545743052421599299352853927 y[1] (numeric) = 0.12125457430524215992993528539258 absolute error = 1.2e-31 relative error = 9.8965338575941937620284222263957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3102 Order of pole (three term test) = -22.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (analytic) = 0.1144906689433075429947118799468 y[1] (numeric) = 0.11449066894330754299471187994676 absolute error = 4e-32 relative error = 3.4937344998662589081522414404844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3028 Order of pole (three term test) = -22.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = 0.1079153129432260569411788432676 y[1] (numeric) = 0.1079153129432260569411788432675 absolute error = 1.0e-31 relative error = 9.2665255071455632204467224053840e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2952 Order of pole (three term test) = -22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = 0.1015291638351182648493854524678 y[1] (numeric) = 0.10152916383511826484938545246773 absolute error = 7e-32 relative error = 6.8945707179937853433072067425026e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2876 Order of pole (three term test) = -22.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.31 y[1] (analytic) = 0.0953328602285732043143891275956 y[1] (numeric) = 0.095332860228573204314389127595498 absolute error = 1.02e-31 relative error = 1.0699353796313405668132907923076e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2798 Order of pole (three term test) = -22.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = 0.0893270217487879607153795448639 y[1] (numeric) = 0.089327021748787960715379544863814 absolute error = 8.6e-32 relative error = 9.6275458776466927692928876742371e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2719 Order of pole (three term test) = -22.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = 0.0835122489746056638597504441363 y[1] (numeric) = 0.08351224897460566385975044413619 absolute error = 1.10e-31 relative error = 1.3171720478207778805825441964067e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2639 Order of pole (three term test) = -23.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (analytic) = 0.077889123378458104150819892807 y[1] (numeric) = 0.07788912337845810415081989280696 absolute error = 4.0e-32 relative error = 5.1355052239633822694625362964229e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2558 Order of pole (three term test) = -23.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (analytic) = 0.0724582072682189739675345810156 y[1] (numeric) = 0.072458207268218973967534581015508 absolute error = 9.2e-32 relative error = 1.2696974361985393374917292370888e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2476 Order of pole (three term test) = -23.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (analytic) = 0.0672200437309735488835647070999 y[1] (numeric) = 0.067220043730973548883564707099784 absolute error = 1.16e-31 relative error = 1.7256757592162900887065564316821e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2393 Order of pole (three term test) = -23.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=80036052, alloc=4586680, time=3.13 x[1] = -0.25 y[1] (analytic) = 0.0621751565787104317108091010116 y[1] (numeric) = 0.062175156578710431710809101011536 absolute error = 6.4e-32 relative error = 1.0293500414265851322428798681076e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = -23.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = 0.0573240502959407901476495060732 y[1] (numeric) = 0.057324050295940790147649506073156 absolute error = 4.4e-32 relative error = 7.6756613974145005655277519831361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2224 Order of pole (three term test) = -23.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (analytic) = 0.0526672099892503260645387038568 y[1] (numeric) = 0.052667209989250326064538703856717 absolute error = 8.3e-32 relative error = 1.5759331093661647744352498966996e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2138 Order of pole (three term test) = -23.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = 0.0482051013387890211879540379106 y[1] (numeric) = 0.048205101338789021187954037910521 absolute error = 7.9e-32 relative error = 1.6388307006095091689100586625267e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2051 Order of pole (three term test) = -23.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (analytic) = 0.0439381705517035101677228638013 y[1] (numeric) = 0.043938170551703510167722863801221 absolute error = 7.9e-32 relative error = 1.7979810949806857837718260131276e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1963 Order of pole (three term test) = -23.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (analytic) = 0.0398668443175167377516069665037 y[1] (numeric) = 0.039866844317516737751606966503576 absolute error = 1.24e-31 relative error = 3.1103540328502184481130251803942e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1875 Order of pole (three term test) = -24.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = 0.0359915297654593620642449916202 y[1] (numeric) = 0.035991529765459362064244991620086 absolute error = 1.14e-31 relative error = 3.1674119089376531013698142054682e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1786 Order of pole (three term test) = -24.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = 0.0323126144237571708145679507769 y[1] (numeric) = 0.032312614423757170814567950776848 absolute error = 5.2e-32 relative error = 1.6092786339742318283115958493891e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1696 Order of pole (three term test) = -24.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (analytic) = 0.028830466180878581656140019575 y[1] (numeric) = 0.028830466180878581656140019574907 absolute error = 9.3e-32 relative error = 3.2257542911907889049799895301939e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1606 Order of pole (three term test) = -24.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (analytic) = 0.0255454332487461019180949519633 y[1] (numeric) = 0.025545433248746101918094951963238 absolute error = 6.2e-32 relative error = 2.4270482867243314885416778874309e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1515 Order of pole (three term test) = -24.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (analytic) = 0.0224578441279154265300380026913 y[1] (numeric) = 0.022457844127915426530038002691236 absolute error = 6.4e-32 relative error = 2.8497837831391424689463186801419e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1423 Order of pole (three term test) = -24.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = 0.0195680075747256562021035459772 y[1] (numeric) = 0.019568007574725656202103545977113 absolute error = 8.7e-32 relative error = 4.4460326207339860698486921192693e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1331 Order of pole (three term test) = -24.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = 0.0168762125704239208109756576964 y[1] (numeric) = 0.016876212570423920810975657696284 absolute error = 1.16e-31 relative error = 6.8735801659249985568151017205301e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1238 Order of pole (three term test) = -24.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = 0.0143827282922674955038036642847 y[1] (numeric) = 0.014382728292267495503803664284646 absolute error = 5.4e-32 relative error = 3.7545032418523621278868981069253e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1145 Order of pole (three term test) = -24.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.11 y[1] (analytic) = 0.0120878040866062992843207771603 y[1] (numeric) = 0.012087804086606299284320777160218 absolute error = 8.2e-32 relative error = 6.7836969736181286235851644389869e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1051 Order of pole (three term test) = -24.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = 0.0099916694439484678088760243923 y[1] (numeric) = 0.0099916694439484678088760243921736 absolute error = 1.264e-31 relative error = 1.2650538602090678808996052298809e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09566 Order of pole (three term test) = -24.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09 y[1] (analytic) = 0.0080945339760114938143212563497 y[1] (numeric) = 0.0080945339760114938143212563496257 absolute error = 7.43e-32 relative error = 9.1790336812707570617057245372510e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0862 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = 0.006396587394761230044586450733 y[1] (numeric) = 0.0063965873947612300445864507328915 absolute error = 1.085e-31 relative error = 1.6962169560734979447542395940044e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07671 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = 0.0048979994934408507581832201205 y[1] (numeric) = 0.0048979994934408507581832201204376 absolute error = 6.24e-32 relative error = 1.2739895151798785121506498978079e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06719 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (analytic) = 0.0035989201295916689046766256343 y[1] (numeric) = 0.0035989201295916689046766256342362 absolute error = 6.38e-32 relative error = 1.7727539846025620402616827434341e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05764 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (analytic) = 0.002499479210067506874258377687 y[1] (numeric) = 0.0024994792100675068742583776868721 absolute error = 1.279e-31 relative error = 5.1170659665757183358298663753132e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04807 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (analytic) = 0.0015997866780441193708584837417 y[1] (numeric) = 0.001599786678044119370858483741645 absolute error = 5.50e-32 relative error = 3.4379583700023281727051855204901e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03848 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = 0.0008999325020249674556825870668 y[1] (numeric) = 0.00089993250202496745568258706668665 absolute error = 1.1335e-31 relative error = 1.2595389070285545905955849247405e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02887 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (analytic) = 0.000399986666844443174608818325 y[1] (numeric) = 0.00039998666684444317460881832496378 absolute error = 3.622e-32 relative error = 9.0553018393700958214473190104746e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01925 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (analytic) = 9.99991666694444394841324956e-05 y[1] (numeric) = 9.9999166669444439484132495500950e-05 absolute error = 9.9050e-32 relative error = 9.9050825420793766377372135589553e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009629 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 0 y[1] (numeric) = -8.57000e-32 absolute error = 8.57000e-32 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=84037128, alloc=4586680, time=3.29 x[1] = 0.01 y[1] (analytic) = 9.99991666694444394841324956e-05 y[1] (numeric) = 9.9999166669444439484132495500954e-05 absolute error = 9.9046e-32 relative error = 9.9046825387460266376710757613356e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.000399986666844443174608818325 y[1] (numeric) = 0.00039998666684444317460881832496377 absolute error = 3.623e-32 relative error = 9.0578019227050958479027158406818e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0008999325020249674556825870668 y[1] (numeric) = 0.00089993250202496745568258706668665 absolute error = 1.1335e-31 relative error = 1.2595389070285545905955849247405e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0015997866780441193708584837417 y[1] (numeric) = 0.001599786678044119370858483741645 absolute error = 5.50e-32 relative error = 3.4379583700023281727051855204901e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.002499479210067506874258377687 y[1] (numeric) = 0.0024994792100675068742583776868721 absolute error = 1.279e-31 relative error = 5.1170659665757183358298663753132e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0035989201295916689046766256343 y[1] (numeric) = 0.0035989201295916689046766256342361 absolute error = 6.39e-32 relative error = 1.7755325958636945826445380455398e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0048979994934408507581832201205 y[1] (numeric) = 0.0048979994934408507581832201204376 absolute error = 6.24e-32 relative error = 1.2739895151798785121506498978079e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.006396587394761230044586450733 y[1] (numeric) = 0.0063965873947612300445864507328915 absolute error = 1.085e-31 relative error = 1.6962169560734979447542395940044e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0080945339760114938143212563497 y[1] (numeric) = 0.0080945339760114938143212563496257 absolute error = 7.43e-32 relative error = 9.1790336812707570617057245372510e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0099916694439484678088760243923 y[1] (numeric) = 0.0099916694439484678088760243921736 absolute error = 1.264e-31 relative error = 1.2650538602090678808996052298809e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.0120878040866062992843207771603 y[1] (numeric) = 0.012087804086606299284320777160218 absolute error = 8.2e-32 relative error = 6.7836969736181286235851644389869e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0143827282922674955038036642847 y[1] (numeric) = 0.014382728292267495503803664284646 absolute error = 5.4e-32 relative error = 3.7545032418523621278868981069253e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0168762125704239208109756576964 y[1] (numeric) = 0.016876212570423920810975657696284 absolute error = 1.16e-31 relative error = 6.8735801659249985568151017205301e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0195680075747256562021035459772 y[1] (numeric) = 0.019568007574725656202103545977113 absolute error = 8.7e-32 relative error = 4.4460326207339860698486921192693e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0224578441279154265300380026913 y[1] (numeric) = 0.022457844127915426530038002691236 absolute error = 6.4e-32 relative error = 2.8497837831391424689463186801419e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0255454332487461019180949519633 y[1] (numeric) = 0.025545433248746101918094951963238 absolute error = 6.2e-32 relative error = 2.4270482867243314885416778874309e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.028830466180878581656140019575 y[1] (numeric) = 0.028830466180878581656140019574907 absolute error = 9.3e-32 relative error = 3.2257542911907889049799895301939e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0323126144237571708145679507769 y[1] (numeric) = 0.032312614423757170814567950776848 absolute error = 5.2e-32 relative error = 1.6092786339742318283115958493891e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0359915297654593620642449916202 y[1] (numeric) = 0.035991529765459362064244991620086 absolute error = 1.14e-31 relative error = 3.1674119089376531013698142054682e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0398668443175167377516069665037 y[1] (numeric) = 0.039866844317516737751606966503576 absolute error = 1.24e-31 relative error = 3.1103540328502184481130251803942e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0439381705517035101677228638013 y[1] (numeric) = 0.043938170551703510167722863801221 absolute error = 7.9e-32 relative error = 1.7979810949806857837718260131276e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.0482051013387890211879540379106 y[1] (numeric) = 0.048205101338789021187954037910521 absolute error = 7.9e-32 relative error = 1.6388307006095091689100586625267e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0526672099892503260645387038568 y[1] (numeric) = 0.052667209989250326064538703856717 absolute error = 8.3e-32 relative error = 1.5759331093661647744352498966996e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.0573240502959407901476495060732 y[1] (numeric) = 0.057324050295940790147649506073156 absolute error = 4.4e-32 relative error = 7.6756613974145005655277519831361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.0621751565787104317108091010116 y[1] (numeric) = 0.062175156578710431710809101011536 absolute error = 6.4e-32 relative error = 1.0293500414265851322428798681076e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.0672200437309735488835647070999 y[1] (numeric) = 0.067220043730973548883564707099785 absolute error = 1.15e-31 relative error = 1.7107992440506324155280516348572e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=88041584, alloc=4586680, time=3.44 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.0724582072682189739675345810156 y[1] (numeric) = 0.072458207268218973967534581015509 absolute error = 9.1e-32 relative error = 1.2558963771094247794755147888596e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.077889123378458104150819892807 y[1] (numeric) = 0.077889123378458104150819892806961 absolute error = 3.9e-32 relative error = 5.0071175933642977127259728890123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.0835122489746056638597504441363 y[1] (numeric) = 0.083512248974605663859750444136191 absolute error = 1.09e-31 relative error = 1.3051977564769526271227028855303e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.0893270217487879607153795448639 y[1] (numeric) = 0.089327021748787960715379544863815 absolute error = 8.5e-32 relative error = 9.5155976697670800626732029338390e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.0953328602285732043143891275956 y[1] (numeric) = 0.095332860228573204314389127595499 absolute error = 1.01e-31 relative error = 1.0594458170859352671386506865006e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.1015291638351182648493854524678 y[1] (numeric) = 0.10152916383511826484938545246773 absolute error = 7e-32 relative error = 6.8945707179937853433072067425026e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.1079153129432260569411788432676 y[1] (numeric) = 0.1079153129432260569411788432675 absolute error = 1.0e-31 relative error = 9.2665255071455632204467224053840e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1144906689433075429947118799468 y[1] (numeric) = 0.11449066894330754299471187994676 absolute error = 4e-32 relative error = 3.4937344998662589081522414404844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1212545743052421599299352853927 y[1] (numeric) = 0.12125457430524215992993528539258 absolute error = 1.2e-31 relative error = 9.8965338575941937620284222263957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1282063526441302832981752637505 y[1] (numeric) = 0.12820635264413028329817526375043 absolute error = 7e-32 relative error = 5.4599478540898054875773198227703e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1353453087879311535923741910182 y[1] (numeric) = 0.13534530878793115359237419101816 absolute error = 4e-32 relative error = 2.9554035051687606846439935225585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1426707288469795010149383845509 y[1] (numeric) = 0.1426707288469795010149383845508 absolute error = 1.0e-31 relative error = 7.0091462213846475281943636390537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1501818802853739170986464942378 y[1] (numeric) = 0.15018188028537391709864649423771 absolute error = 9e-32 relative error = 5.9927335993518668072625469029424e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1578780119942298344029465358964 y[1] (numeric) = 0.15787801199422983440294653589631 absolute error = 9e-32 relative error = 5.7006038309685165538307241611507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.165758354366789789048715883446 y[1] (numeric) = 0.16575835436678978904871588344588 absolute error = 1.2e-31 relative error = 7.2394541112820301877213695380697e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1738221193753834551278224206687 y[1] (numeric) = 0.17382211937538345512782242066858 absolute error = 1.2e-31 relative error = 6.9036093007731616010457240758315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1820685006502297550481790446731 y[1] (numeric) = 0.18206850065022975504817904467302 absolute error = 8e-32 relative error = 4.3939506127799293637192063319412e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1904966735600731656689252220033 y[1] (numeric) = 0.19049667356007316566892522200317 absolute error = 1.3e-31 relative error = 6.8242661444166621068982618367850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.1991057952946461566623187770271 y[1] (numeric) = 0.19910579529464615666231877702702 absolute error = 8e-32 relative error = 4.0179644134221318268471330804715e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2078950049489495149272201929992 y[1] (numeric) = 0.2078950049489495149272201929991 absolute error = 1.0e-31 relative error = 4.8101203790132378534399575722065e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2168634236093421270919614469332 y[1] (numeric) = 0.21686342360934212709196144693313 absolute error = 7e-32 relative error = 3.2278380021380660669038855020917e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2260101544414316112000903376825 y[1] (numeric) = 0.22601015444143161120009033768243 absolute error = 7e-32 relative error = 3.0972059716962777596955697711048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2353342827797570085890636817267 y[1] (numeric) = 0.2353342827797570085890636817266 absolute error = 1.0e-31 relative error = 4.2492746411107172102283847733567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2448348762192545677674368347923 y[1] (numeric) = 0.24483487621925456776743683479226 absolute error = 4e-32 relative error = 1.6337541700627321395365592147389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.254510984708497473788383052849 y[1] (numeric) = 0.2545109847084974737883830528489 absolute error = 1.0e-31 relative error = 3.9291034968307697802240923805290e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.264361640644700199224304856023 y[1] (numeric) = 0.26436164064470019922430485602289 absolute error = 1.1e-31 relative error = 4.1609667624902913268990099902670e-29 % Correct digits = 31 h = 0.01 bytes used=92042276, alloc=4586680, time=3.61 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.2743858589704779763866099628716 y[1] (numeric) = 0.27438585897047797638660996287151 absolute error = 9e-32 relative error = 3.2800524173398957302601570098463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2845826372723517149240624421644 y[1] (numeric) = 0.28458263727235171492406244216432 absolute error = 8e-32 relative error = 2.8111342549488806823548260918642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.2949509558809885143900364047645 y[1] (numeric) = 0.29495095588098851439003640476437 absolute error = 1.3e-31 relative error = 4.4075124154693182293308540874674e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.3054897779731677478109489922674 y[1] (numeric) = 0.30548977797316774781094899226728 absolute error = 1.2e-31 relative error = 3.9281183415092869718469400940943e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.316198049675462519732487272168 y[1] (numeric) = 0.31619804967546251973248727216789 absolute error = 1.1e-31 relative error = 3.4788323366605565113793730026194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0.3270747001696261306842253439 y[1] (numeric) = 0.32707470016962613068422534389988 absolute error = 1.2e-31 relative error = 3.6688866469270198953411804550964e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.3381186417996730095040069550186 y[1] (numeric) = 0.33811864179967300950400695501856 absolute error = 4e-32 relative error = 1.1830167005018024865899752349615e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.3493287701806434055180950020892 y[1] (numeric) = 0.34932877018064340551809500208916 absolute error = 4e-32 relative error = 1.1450531251495652762119910506332e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0.3607039643090409641985068426904 y[1] (numeric) = 0.36070396430904096419850684269027 absolute error = 1.3e-31 relative error = 3.6040635219805811009453024937638e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.3722430866749321426320006912786 y[1] (numeric) = 0.37224308667493214263200069127852 absolute error = 8e-32 relative error = 2.1491332643569392745843102485924e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.3839449833756962549525820684459 y[1] (numeric) = 0.3839449833756962549525820684458 absolute error = 1.0e-31 relative error = 2.6045398254923522250782259318448e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0.3958084842314147728277784414794 y[1] (numeric) = 0.39580848423141477282777844147926 absolute error = 1.4e-31 relative error = 3.5370641504022715772746780355275e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.4078324029018883421647908586402 y[1] (numeric) = 0.4078324029018883421647908586401 absolute error = 1.0e-31 relative error = 2.4519876127659443717125723925415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.4200155370052698144323658175395 y[1] (numeric) = 0.42001553700526981443236581753942 absolute error = 8e-32 relative error = 1.9046914447594890508424281083038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0.4323566682383014293941157103238 y[1] (numeric) = 0.43235666823830142939411571032367 absolute error = 1.3e-31 relative error = 3.0067768014242370614983486229747e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.4448545624981441256352118319114 y[1] (numeric) = 0.44485456249814412563521183191127 absolute error = 1.3e-31 relative error = 2.9223033988898864625315224739971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0.4575079700057867960529213690045 y[1] (numeric) = 0.45750797000578679605292136900437 absolute error = 1.3e-31 relative error = 2.8414805538438093910070327699040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.4703156254310231474882800196163 y[1] (numeric) = 0.47031562543102314748828001961618 absolute error = 1.2e-31 relative error = 2.5514780609303675493037244369476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.4832762480189836669170841117209 y[1] (numeric) = 0.4832762480189836669170841117208 absolute error = 1.0e-31 relative error = 2.0692099065475256055881542758270e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.4963885417182100411090260754961 y[1] (numeric) = 0.49638854171821004110902607549601 absolute error = 9e-32 relative error = 1.8130958399739053650671143613172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.5096511953102592224197356828993 y[1] (numeric) = 0.50965119531025922241973568289924 absolute error = 6e-32 relative error = 1.1772757633477918894904451788035e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.5230628825408241804171508786023 y[1] (numeric) = 0.52306288254082418041715087860225 absolute error = 5e-32 relative error = 9.5590801161651121148243125131636e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0.5366222622523582273763224939998 y[1] (numeric) = 0.53662226225235822737632249399974 absolute error = 6e-32 relative error = 1.1181049356424892793965828082818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.550327978518189655320623266666 y[1] (numeric) = 0.5503279785181896553206232666659 absolute error = 1.0e-31 relative error = 1.8170982378409961385780431705115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.5641786607781132732574188693513 y[1] (numeric) = 0.56417866077811327325741886935123 absolute error = 7e-32 relative error = 1.2407417165239153173367949433388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) 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=96043192, alloc=4586680, time=3.76 x[1] = 0.78 y[1] (analytic) = 0.5781729239754452855674699524709 y[1] (numeric) = 0.57817292397544528556746995247079 absolute error = 1.1e-31 relative error = 1.9025449902367210279987157478748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0.5923093686955278061744382778301 y[1] (numeric) = 0.59230936869552780617443827783001 absolute error = 9e-32 relative error = 1.5194762189598899588780390859207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0.6065865813056691581585000367154 y[1] (numeric) = 0.60658658130566915815850003671526 absolute error = 1.4e-31 relative error = 2.3079969836894834061013925844631e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0.6210031340965059649007215186398 y[1] (numeric) = 0.6210031340965059649007215186397 absolute error = 1.0e-31 relative error = 1.6102978311935486206791468653127e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed NO 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) = 0.6355575854247728966668840431261 y[1] (numeric) = 0.63555758542477289666688404312604 absolute error = 6e-32 relative error = 9.4405292889233931931997180235529e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0.6502484798574657957750741642711 y[1] (numeric) = 0.65024847985746579577507416427099 absolute error = 1.1e-31 relative error = 1.6916610097129631980651023502541e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0.6650743483173837641546579262583 y[1] (numeric) = 0.66507434831738376415465792625818 absolute error = 1.2e-31 relative error = 1.8043095528130960817450923596830e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0.6800337082300356592091679410771 y[1] (numeric) = 0.68003370823003565920916794107696 absolute error = 1.4e-31 relative error = 2.0587214766807127860545415333172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0.6951250636718963074559386715523 y[1] (numeric) = 0.69512506367189630745593867155218 absolute error = 1.2e-31 relative error = 1.7263080598204527536582465424132e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0.7103469055199976104446723890343 y[1] (numeric) = 0.71034690551999761044467238903424 absolute error = 6e-32 relative error = 8.4465772334262511106203491288066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0.7256977116028395839690027885558 y[1] (numeric) = 0.72569771160283958396900278855572 absolute error = 8e-32 relative error = 1.1023873814250424852298438568138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0.7411759468526062395928938852395 y[1] (numeric) = 0.7411759468526062395928938852394 absolute error = 1.0e-31 relative error = 1.3492073025932461052975142446580e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed NO 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) = 0.7567800634586710870305676971857 y[1] (numeric) = 0.75678006345867108703056769718564 absolute error = 6e-32 relative error = 7.9283272508243990586341603069717e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0.7725085010223769069576435476506 y[1] (numeric) = 0.77250850102237690695764354765055 absolute error = 5e-32 relative error = 6.4724206832452284490527487969442e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0.7883596867130743164051905866512 y[1] (numeric) = 0.78835968671307431640519058665116 absolute error = 4e-32 relative error = 5.0738261575465502445145563276439e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0.804332035425403523010185831134 y[1] (numeric) = 0.80433203542540352301018583113394 absolute error = 6e-32 relative error = 7.4596059037069900719489127119070e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0.820423949937803540078020369552 y[1] (numeric) = 0.82042394993780354007802036955188 absolute error = 1.2e-31 relative error = 1.4626584220158031416860171730186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0.8366338210722330116676380524791 y[1] (numeric) = 0.836633821072233011667638052479 absolute error = 1.0e-31 relative error = 1.1952660468810551870932661342232e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0.8529600278550866757498983992963 y[1] (numeric) = 0.8529600278550866757498983992962 absolute error = 1.0e-31 relative error = 1.1723878814282427607595940143299e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0.8694009376792913739269444903003 y[1] (numeric) = 0.86940093767929137392694449030019 absolute error = 1.1e-31 relative error = 1.2652390310691993655385346751819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0.8859549064675653982466834652801 y[1] (numeric) = 0.88595490646756539824668346528004 absolute error = 6e-32 relative error = 6.7723537125866784683813290949933e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0.9026202788368248493137471826928 y[1] (numeric) = 0.90262027883682484931374718269269 absolute error = 1.1e-31 relative error = 1.2186741487987966397857592666707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0.919395388263720565198126785114 y[1] (numeric) = 0.91939538826372056519812678511396 absolute error = 4e-32 relative error = 4.3506852993400428215535735193124e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0.9362785572512890675865372884416 y[1] (numeric) = 0.93627855725128906758653728844156 absolute error = 4e-32 relative error = 4.2722328403452206724382620604507e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0.9532680974967008602207723839324 y[1] (numeric) = 0.9532680974967008602207723839323 absolute error = 1.0e-31 relative error = 1.0490228327435041147559458031489e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=100046560, alloc=4586680, time=3.92 x[1] = 1.03 y[1] (analytic) = 0.9703623100600893049329954003253 y[1] (numeric) = 0.97036231006008930493299540032522 absolute error = 8e-32 relative error = 8.2443432901929209740878156989499e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0.9875594855344431925310531580157 y[1] (numeric) = 0.98755948553444319253105315801557 absolute error = 1.3e-31 relative error = 1.3163763996418621754241666546042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0048579042165460194183008543758 y[1] (numeric) = 1.0048579042165460194183008543757 absolute error = 1e-31 relative error = 9.9516558092824719900684299305615e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 1.0222558362789448761627249200872 y[1] (numeric) = 1.0222558362789448761627249200871 absolute error = 1e-31 relative error = 9.7822870216133265079915273219518e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 1.0397515419429317512698138636482 y[1] (numeric) = 1.0397515419429317512698138636481 absolute error = 1e-31 relative error = 9.6176822987090739853220028140128e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 1.0573432716525199521729504229479 y[1] (numeric) = 1.0573432716525199521729504229479 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 1.0750292662493982459442058522497 y[1] (numeric) = 1.0750292662493982459442058522497 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 1.0928077571488452244572598964306 y[1] (numeric) = 1.0928077571488452244572598964306 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 1.1106769665165863027125249761329 y[1] (numeric) = 1.1106769665165863027125249761329 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 1.1286351074465756647720224120777 y[1] (numeric) = 1.1286351074465756647720224120778 absolute error = 1e-31 relative error = 8.8602595595524246767385107136981e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 1.1466803841396853792575683286929 y[1] (numeric) = 1.146680384139685379257568328693 absolute error = 1e-31 relative error = 8.7208259060807550413890072911428e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 1.1648109920832838156496265183548 y[1] (numeric) = 1.1648109920832838156496265183549 absolute error = 1e-31 relative error = 8.5850838187188067520444821235886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 1.1830251182316854036948465623802 y[1] (numeric) = 1.1830251182316854036948465623802 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 1.201320941187453691096720753212 y[1] (numeric) = 1.201320941187453691096720753212 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 1.219696631383539569334676129899 y[1] (numeric) = 1.219696631383539569334676129899 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 1.2381503512662364539408010665745 y[1] (numeric) = 1.2381503512662364539408010665745 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 1.2566802554789341238686408832991 y[1] (numeric) = 1.2566802554789341238686408832991 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.2752844910466528447232532887538 y[1] (numeric) = 1.2752844910466528447232532887539 absolute error = 1e-31 relative error = 7.8413876042613749324452115264341e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 1.2939611975613393225939785726704 y[1] (numeric) = 1.2939611975613393225939785726705 absolute error = 1e-31 relative error = 7.7282070118072122615019220736677e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 1.3127085073679059590489540511296 y[1] (numeric) = 1.3127085073679059590489540511297 absolute error = 1e-31 relative error = 7.6178374283951770071276414522781e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 1.3315245457509948035209055090047 y[1] (numeric) = 1.3315245457509948035209055090048 absolute error = 1e-31 relative error = 7.5101882514376688788012953675962e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 1.3504074311224475268446131686052 y[1] (numeric) = 1.3504074311224475268446131686054 absolute error = 2e-31 relative error = 1.4810345040367679876971585634013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 1.3693552752094626691049228951239 y[1] (numeric) = 1.3693552752094626691049228951241 absolute error = 2e-31 relative error = 1.4605413483320251647917090647585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.388366183243421346227315021647 y[1] (numeric) = 1.3883661832434213462273150216472 absolute error = 2e-31 relative error = 1.4405421452485358408549029259662e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 1.4074382541493625328977259678241 y[1] (numeric) = 1.4074382541493625328977259678242 absolute error = 1e-31 relative error = 7.1051074322573892164562257413270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 1.4265695807360889744412262128148 y[1] (numeric) = 1.4265695807360889744412262128149 bytes used=104048216, alloc=4586680, time=4.08 absolute error = 1e-31 relative error = 7.0098228190454942338768340448648e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 1.4457582498868847172267878198776 y[1] (numeric) = 1.4457582498868847172267878198777 absolute error = 1e-31 relative error = 6.9167857079718508756487805043211e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.4650023427508251860040317814143 y[1] (numeric) = 1.4650023427508251860040317814143 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 1.4842999349346606773236460427676 y[1] (numeric) = 1.4842999349346606773236460427677 absolute error = 1e-31 relative error = 6.7371828056033721791309668084476e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 1.5036490966952540808520345411453 y[1] (numeric) = 1.5036490966952540808520345411454 absolute error = 1e-31 relative error = 6.6504878179211974899052810592204e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 1.5230478931325535849684300279788 y[1] (numeric) = 1.523047893132553584968430027979 absolute error = 2e-31 relative error = 1.3131563419758701043336584972065e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 1.5424943843830810695347210153997 y[1] (numeric) = 1.5424943843830810695347210153999 absolute error = 2e-31 relative error = 1.2966011547587564136473778370063e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5619866258139168371599556539787 y[1] (numeric) = 1.5619866258139168371599556539789 absolute error = 2e-31 relative error = 1.2804206943563579094125206673888e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5815226682171612846480494952163 y[1] (numeric) = 1.5815226682171612846480494952164 absolute error = 1e-31 relative error = 6.3230203404374377136748436188494e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 1.6011005580048540686236032207094 y[1] (numeric) = 1.6011005580048540686236032207095 absolute error = 1e-31 relative error = 6.2457039003603188580394865616551e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 1.6207183374043312735816998528036 y[1] (numeric) = 1.6207183374043312735816998528037 absolute error = 1e-31 relative error = 6.1701035702573371731443904707241e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 1.6403740446540010468076735643919 y[1] (numeric) = 1.640374044654001046807673564392 absolute error = 1e-31 relative error = 6.0961705853552862335216849455541e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.6600657141995181227665039295927 y[1] (numeric) = 1.6600657141995181227665039295928 absolute error = 1e-31 relative error = 6.0238579198787856996928782077488e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 1.6797913768903376196728749012782 y[1] (numeric) = 1.6797913768903376196728749012783 absolute error = 1e-31 relative error = 5.9531202133637535234061342931929e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 1.6995490601766284530260357940482 y[1] (numeric) = 1.6995490601766284530260357940483 absolute error = 1e-31 relative error = 5.8839137005911046929859710123407e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 1.7193367883065266749322047508502 y[1] (numeric) = 1.7193367883065266749322047508503 absolute error = 1e-31 relative error = 5.8161961449388708915000429189470e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 1.7391525825237090140449596877417 y[1] (numeric) = 1.7391525825237090140449596877418 absolute error = 1e-31 relative error = 5.7499267749635043337750961905158e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 1.758994461265266858934266745504 y[1] (numeric) = 1.7589944612652668589342667455041 absolute error = 1e-31 relative error = 5.6850662240328341431414647751480e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 1.7788604403598608976507037817533 y[1] (numeric) = 1.7788604403598608976507037817534 absolute error = 1e-31 relative error = 5.6215764728440497806957037250832e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 1.7987485332261365981860507970752 y[1] (numeric) = 1.7987485332261365981860507970753 absolute error = 1e-31 relative error = 5.5594207946702528282804041199949e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 1.8186567510713806884475469187043 y[1] (numeric) = 1.8186567510713806884475469187044 absolute error = 1e-31 relative error = 5.4985637031886006164742764323742e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 1.8385831030903987702633630308726 y[1] (numeric) = 1.8385831030903987702633630308726 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 1.8585255966645941798236202971315 y[1] (numeric) = 1.8585255966645941798236202971315 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 1.8784822375612281868368089701676 y[1] (numeric) = 1.8784822375612281868368089701677 absolute error = 1e-31 relative error = 5.3234466635056776857444663670241e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 1.8984510301328416065477414596946 y[1] (numeric) = 1.8984510301328416065477414596946 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 1.9184299775168178826220219858478 y[1] (numeric) = 1.9184299775168178826220219858478 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 bytes used=108048988, alloc=4586680, time=4.24 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9384170818350676847550463858472 y[1] (numeric) = 1.9384170818350676847550463858472 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 1.9584103443938150527121744506089 y[1] (numeric) = 1.9584103443938150527121744506089 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 1.9784077658834651083521586724782 y[1] (numeric) = 1.9784077658834651083521586724782 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 1.9984073465785333490291829327093 y[1] (numeric) = 1.9984073465785333490291829327093 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 2.0184070865376165296107781139655 y[1] (numeric) = 2.0184070865376165296107781139655 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -0.8949 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 2.0384049858033851361900546924868 y[1] (numeric) = 2.0384049858033851361900546924869 absolute error = 1e-31 relative error = 4.9057964779549222052346453525071e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01851 Order of pole (three term test) = -0.9018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 2.058399044602577452411540925893 y[1] (numeric) = 2.0583990446025774524115409258931 absolute error = 1e-31 relative error = 4.8581445012916512328911384808379e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -0.9135 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 2.078387263545975219170655219202 y[1] (numeric) = 2.0783872635459752191706552192021 absolute error = 1e-31 relative error = 4.8114228639655988631429947945682e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03776 Order of pole (three term test) = -0.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 2.0983676438283408902874885494247 y[1] (numeric) = 2.0983676438283408902874885494247 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04737 Order of pole (three term test) = -0.9513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 2.1183381874282964905959433948396 y[1] (numeric) = 2.1183381874282964905959433948396 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05696 Order of pole (three term test) = -0.9775 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 2.1382968973081240887289854149132 y[1] (numeric) = 2.1382968973081240887289854149132 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06652 Order of pole (three term test) = -1.008 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 2.1582417776134679047192291946826 y[1] (numeric) = 2.1582417776134679047192291946825 absolute error = 1e-31 relative error = 4.6334011804079525452219666154322e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07606 Order of pole (three term test) = -1.044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 2.1781708338729180823705158633012 y[1] (numeric) = 2.1781708338729180823705158633012 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08556 Order of pole (three term test) = -1.085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 2.1980820731974561681895646848972 y[1] (numeric) = 2.1980820731974561681895646848972 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09503 Order of pole (three term test) = -1.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 2.2179735044797423524960094683456 y[1] (numeric) = 2.2179735044797423524960094683456 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = -1.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 2.2378431385932245441527809396662 y[1] (numeric) = 2.2378431385932245441527809396661 absolute error = 1e-31 relative error = 4.4685884490931301612438331253267e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -1.235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 2.2576889885910493681752857146697 y[1] (numeric) = 2.2576889885910493681752857146697 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1232 Order of pole (three term test) = -1.294 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 2.2775090699047551952853795661022 y[1] (numeric) = 2.2775090699047551952853795661022 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1325 Order of pole (three term test) = -1.358 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 2.2973014005427273342727565606624 y[1] (numeric) = 2.2973014005427273342727565606624 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1417 Order of pole (three term test) = -1.427 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 2.3170640012883955418098967026851 y[1] (numeric) = 2.3170640012883955418098967026852 absolute error = 1e-31 relative error = 4.3158065527924710228410789426906e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1509 Order of pole (three term test) = -1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 2.3367948958981540301347546306902 y[1] (numeric) = 2.3367948958981540301347546306902 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1601 Order of pole (three term test) = -1.578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 2.3564921112989841807653538878853 y[1] (numeric) = 2.3564921112989841807653538878853 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 Order of pole (three term test) = -1.661 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 2.3761536777857602021396003530082 y[1] (numeric) = 2.3761536777857602021396003530082 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1781 Order of pole (three term test) = -1.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 2.3957776292182180007789716834608 y[1] (numeric) = 2.3957776292182180007789716834608 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.187 Order of pole (three term test) = -1.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 2.4153620032175675692531065806253 y[1] (numeric) = 2.4153620032175675692531065806253 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1959 Order of pole (three term test) = -1.936 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=112050708, alloc=4586680, time=4.40 x[1] = 1.79 y[1] (analytic) = 2.4349048413627292298703405289292 y[1] (numeric) = 2.4349048413627292298703405289293 absolute error = 1e-31 relative error = 4.1069366778224307706024289953838e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2047 Order of pole (three term test) = -2.036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 2.4544041893861741106333486130612 y[1] (numeric) = 2.4544041893861741106333486130612 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2133 Order of pole (three term test) = -2.141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 2.473858097369349269575499701684 y[1] (numeric) = 2.473858097369349269575499701684 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2219 Order of pole (three term test) = -2.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 2.4932646199376679251283420896617 y[1] (numeric) = 2.4932646199376679251283420896618 absolute error = 1e-31 relative error = 4.0108057203531014860575542763424e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = -2.363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 2.5126218164550452936596751672371 y[1] (numeric) = 2.5126218164550452936596751672371 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2389 Order of pole (three term test) = -2.481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 2.5319277512179605807605659665632 y[1] (numeric) = 2.5319277512179605807605659665632 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2472 Order of pole (three term test) = -2.603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 2.5511804936490257202438996709496 y[1] (numeric) = 2.5511804936490257202438996709496 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = -2.729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 2.5703781184900415041418709765782 y[1] (numeric) = 2.5703781184900415041418709765782 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2636 Order of pole (three term test) = -2.859 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 2.5895187059945217982502961296198 y[1] (numeric) = 2.5895187059945217982502961296197 absolute error = 1e-31 relative error = 3.8617214762151848650703939108721e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 Order of pole (three term test) = -2.993 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 2.6086003421196665909586275190445 y[1] (numeric) = 2.6086003421196665909586275190444 absolute error = 1e-31 relative error = 3.8334733912801355094412915485393e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2795 Order of pole (three term test) = -3.131 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 2.6276211187177646782207648311025 y[1] (numeric) = 2.6276211187177646782207648311024 absolute error = 1e-31 relative error = 3.8057237128919991972065356930738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2873 Order of pole (three term test) = -3.273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 2.6465791337270068445576673901606 y[1] (numeric) = 2.6465791337270068445576673901606 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.295 Order of pole (three term test) = -3.419 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 2.6654724913616904589326778787951 y[1] (numeric) = 2.665472491361690458932677878795 absolute error = 1e-31 relative error = 3.7516800613805521044601510372439e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3025 Order of pole (three term test) = -3.569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 2.6842993023017964651984732063181 y[1] (numeric) = 2.684299302301796465198473206318 absolute error = 1e-31 relative error = 3.7253669855015658802300488155690e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = -3.723 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 2.7030576838819198095745781294237 y[1] (numeric) = 2.7030576838819198095745781294237 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = -3.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 2.7217457602795344122701353716815 y[1] (numeric) = 2.7217457602795344122701353716814 absolute error = 1e-31 relative error = 3.6741124560337182757247065485320e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3245 Order of pole (three term test) = -4.041 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 2.7403616627025738569116569182614 y[1] (numeric) = 2.7403616627025738569116569182613 absolute error = 1e-31 relative error = 3.6491533712881873770250850161475e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3315 Order of pole (three term test) = -4.205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 2.7589035295763090398631304308949 y[1] (numeric) = 2.7589035295763090398631304308948 absolute error = 1e-31 relative error = 3.6246283687692850477099479166557e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 2.7773695067295040918292796277586 y[1] (numeric) = 2.7773695067295040918292796277585 absolute error = 1e-31 relative error = 3.6005291970586643353154586295515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3453 Order of pole (three term test) = -4.545 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 2.7957577475798319563049477198144 y[1] (numeric) = 2.7957577475798319563049477198143 absolute error = 1e-31 relative error = 3.5768478183263813851804127894301e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3519 Order of pole (three term test) = -4.719 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 2.8140664133185310834672714322606 y[1] (numeric) = 2.8140664133185310834672714322605 absolute error = 1e-31 relative error = 3.5535764019895131943677237842610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3584 Order of pole (three term test) = -4.898 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 2.8322936730942847739951364590015 y[1] (numeric) = 2.8322936730942847739951364590014 absolute error = 1e-31 relative error = 3.5307073185934797865233375113541e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3648 Order of pole (three term test) = -5.079 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 2.8504377041963047850347646803309 y[1] (numeric) = 2.8504377041963047850347646803307 absolute error = 2e-31 relative error = 7.0164662678145075846895250940217e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.371 Order of pole (three term test) = -5.263 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 2.8684966922366008901034057481804 y[1] (numeric) = 2.8684966922366008901034057481802 absolute error = 2e-31 relative error = 6.9722932064480655922933373027362e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3771 Order of pole (three term test) = -5.451 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 2.8864688313314181661270334633922 y[1] (numeric) = 2.886468831331418166127033463392 absolute error = 2e-31 relative error = 6.9288813317186458320463911419724e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.383 Order of pole (three term test) = -5.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=116052852, alloc=4586680, time=4.56 x[1] = 2.04 y[1] (analytic) = 2.9043523242818238640345404105827 y[1] (numeric) = 2.9043523242818238640345404105825 absolute error = 2e-31 relative error = 6.8862168796774739201336023816658e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 Order of pole (three term test) = -5.835 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 2.9221453827534258043718599883348 y[1] (numeric) = 2.9221453827534258043718599883346 absolute error = 2e-31 relative error = 6.8442864335362962404659396814740e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = -6.031 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 2.9398462274552043262462192529758 y[1] (numeric) = 2.9398462274552043262462192529756 absolute error = 2e-31 relative error = 6.8030769137583228964823791728797e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3999 Order of pole (three term test) = -6.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 2.9574530883174399065546542780235 y[1] (numeric) = 2.9574530883174399065546542780233 absolute error = 2e-31 relative error = 6.7625755684863423414244559118891e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -6.432 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 2.9749642046687186568831376995447 y[1] (numeric) = 2.9749642046687186568831376995445 absolute error = 2e-31 relative error = 6.7227699642951261200930616887466e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4103 Order of pole (three term test) = -6.636 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 2.9923778254119979976741326237409 y[1] (numeric) = 2.9923778254119979976741326237407 absolute error = 2e-31 relative error = 6.6836479772557967061568654196788e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = -6.843 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 3.0096922091997149032418770474383 y[1] (numeric) = 3.0096922091997149032418770474381 absolute error = 2e-31 relative error = 6.6451977843003596543135145315664e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4201 Order of pole (three term test) = -7.053 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 3.0269056246079192069568203141434 y[1] (numeric) = 3.0269056246079192069568203141431 absolute error = 3e-31 relative error = 9.9111117823126568630790226801547e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4247 Order of pole (three term test) = -7.265 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 3.0440163503094145534138037659678 y[1] (numeric) = 3.0440163503094145534138037659675 absolute error = 3e-31 relative error = 9.8554004143080886152574857721327e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -7.479 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 3.0610226752458896836330524192194 y[1] (numeric) = 3.0610226752458896836330524192192 absolute error = 2e-31 relative error = 6.5337640788281370106884122386484e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -7.695 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 3.0779228987990228403088998240172 y[1] (numeric) = 3.077922898799022840308899824017 absolute error = 2e-31 relative error = 6.4978885623820582866578271218755e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -7.913 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 3.0947153309605421828083077645281 y[1] (numeric) = 3.0947153309605421828083077645279 absolute error = 2e-31 relative error = 6.4626299549795332278143991409161e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -8.133 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 3.1113982925012252060193974879667 y[1] (numeric) = 3.1113982925012252060193974879666 absolute error = 1e-31 relative error = 3.2139890364088004979472792474441e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4453 Order of pole (three term test) = -8.356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 3.127970115138820263248939988833 y[1] (numeric) = 3.1279701151388202632489399888329 absolute error = 1e-31 relative error = 3.1969614900096949821274525547725e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4489 Order of pole (three term test) = -8.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 3.144429141704873401156449735325 y[1] (numeric) = 3.1444291417048734011564497353249 absolute error = 1e-31 relative error = 3.1802274910154644925282756913345e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -8.806 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 3.1607737263104438241804103275939 y[1] (numeric) = 3.1607737263104438241804103275938 absolute error = 1e-31 relative error = 3.1637823096159915753895002482284e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4555 Order of pole (three term test) = -9.033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 3.1770022345106914170482852253099 y[1] (numeric) = 3.1770022345106914170482852253098 absolute error = 1e-31 relative error = 3.1476213303766083541440031391683e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -9.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 3.1931130434683198667552183550373 y[1] (numeric) = 3.1931130434683198667552183550372 absolute error = 1e-31 relative error = 3.1317400492461500109268327139118e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -9.493 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 3.2091045421158590398354288750003 y[1] (numeric) = 3.2091045421158590398354288750002 absolute error = 1e-31 relative error = 3.1161340706609388166746601279342e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = -9.725 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 3.2249751313167703868238078213713 y[1] (numeric) = 3.2249751313167703868238078213712 absolute error = 1e-31 relative error = 3.1007991047413006138087274507528e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4666 Order of pole (three term test) = -9.958 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 3.2407232240253592635015245326209 y[1] (numeric) = 3.2407232240253592635015245326208 absolute error = 1e-31 relative error = 3.0857309645773526679223962786792e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4689 Order of pole (three term test) = -10.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 3.2563472454454781778267781147928 y[1] (numeric) = 3.2563472454454781778267781147927 absolute error = 1e-31 relative error = 3.0709255636009327609916444491444e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -10.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 3.2718456331880050923582531374897 y[1] (numeric) = 3.2718456331880050923582531374896 absolute error = 1e-31 relative error = 3.0563789130406645930449899432921e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -10.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 3.2872168374270810344722686962486 y[1] (numeric) = 3.2872168374270810344722686962485 absolute error = 1e-31 relative error = 3.0420871194572742710940985812731e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -10.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 3.3024593210550913907427967009214 y[1] (numeric) = 3.3024593210550913907427967009213 absolute error = 1e-31 relative error = 3.0280463823563871579214199480644e-30 % Correct digits = 32 h = 0.01 bytes used=120053832, alloc=4586680, time=4.72 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -11.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 3.3175715598363753874840620363779 y[1] (numeric) = 3.3175715598363753874840620363778 absolute error = 1e-31 relative error = 3.0142529918761438797180732839552e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = -11.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 3.332552042559648386635761142332 y[1] (numeric) = 3.3325520425596483866357611423319 absolute error = 1e-31 relative error = 3.0007033265470790882026878968656e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -11.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 3.3473992711891217548883286469421 y[1] (numeric) = 3.3473992711891217548883286469419 absolute error = 2e-31 relative error = 5.9747877022436137301370891529831e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -11.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 3.3621117610143051941872723320165 y[1] (numeric) = 3.3621117610143051941872723320163 absolute error = 2e-31 relative error = 5.9486422289443053162575529251449e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 3.376688040798476553508360855632 y[1] (numeric) = 3.3766880407984765535083608556318 absolute error = 2e-31 relative error = 5.9229634951029271042386194477562e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 3.3911266529258042750462111441227 y[1] (numeric) = 3.3911266529258042750462111441225 absolute error = 2e-31 relative error = 5.8977449228398333903639749891255e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 3.4054261535471077626942582245178 y[1] (numeric) = 3.4054261535471077626942582245176 absolute error = 2e-31 relative error = 5.8729800906614600144143213143081e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 3.4195851127242410969007260692902 y[1] (numeric) = 3.41958511272424109690072606929 absolute error = 2e-31 relative error = 5.8486627297505201236830886365964e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 3.4336021145730856576494332176447 y[1] (numeric) = 3.4336021145730856576494332176445 absolute error = 2e-31 relative error = 5.8247867203700988494000608702539e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 3.4474757574051373564222952147351 y[1] (numeric) = 3.4474757574051373564222952147349 absolute error = 2e-31 relative error = 5.8013460883779198050684788468116e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 3.4612046538676743185383165852361 y[1] (numeric) = 3.461204653867674318538316585236 absolute error = 1e-31 relative error = 2.8891675009235992603679955986649e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 3.4747874310824909992176444546696 y[1] (numeric) = 3.4747874310824909992176444546694 absolute error = 2e-31 relative error = 5.7557477677906342741661148744220e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 3.4882227307831848600746887911359 y[1] (numeric) = 3.4882227307831848600746887911357 absolute error = 2e-31 relative error = 5.7335788289842225376172563550861e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -14.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 3.5015092094509818774870651378215 y[1] (numeric) = 3.5015092094509818774870651378213 absolute error = 2e-31 relative error = 5.7118227608876956826023058660508e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -14.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 3.5146455384490873004027104883558 y[1] (numeric) = 3.5146455384490873004027104883556 absolute error = 2e-31 relative error = 5.6904742686585199172016922170432e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -14.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 3.5276304041555482226213501850748 y[1] (numeric) = 3.5276304041555482226213501850746 absolute error = 2e-31 relative error = 5.6695281842564919019893025919485e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -14.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 3.540462508094614683403806134673 y[1] (numeric) = 3.5404625080946146834038061346728 absolute error = 2e-31 relative error = 5.6489794636360893209304587330155e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -15.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 3.5531405670665861604085526293724 y[1] (numeric) = 3.5531405670665861604085526293722 absolute error = 2e-31 relative error = 5.6288231840238360816185544664803e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -15.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 3.5656633132761304704144311681231 y[1] (numeric) = 3.5656633132761304704144311681229 absolute error = 2e-31 relative error = 5.6090545412780449837543851163792e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -15.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 3.5780294944590622460463840671807 y[1] (numeric) = 3.5780294944590622460463840671805 absolute error = 2e-31 relative error = 5.5896688473283988151188567494283e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -15.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 3.5902378740075683107621826651431 y[1] (numeric) = 3.590237874007568310762182665143 absolute error = 1e-31 relative error = 2.7853307638464625453404546069250e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = -16.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 3.6022872310938674296670055809347 y[1] (numeric) = 3.6022872310938674296670055809346 absolute error = 1e-31 relative error = 2.7760140595350051072903962067798e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -16.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 3.6141763607922920702838350157568 y[1] (numeric) = 3.6141763607922920702838350157567 absolute error = 1e-31 relative error = 2.7668821335015929400347991173521e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 3.6259040741997799652053285209037 y[1] (numeric) = 3.6259040741997799652053285209036 absolute error = 1e-31 relative error = 2.7579328618082520924488514984891e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4561 Order of pole (three term test) = -16.86 NO COMPLEX POLE (six term test) for Equation 1 bytes used=124054948, alloc=4586680, time=4.88 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 3.63746919855476342757131034511 y[1] (numeric) = 3.6374691985547634275713103451099 absolute error = 1e-31 relative error = 2.7491641727091991888233712683959e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4529 Order of pole (three term test) = -17.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 3.6488705773544445305394087116131 y[1] (numeric) = 3.648870577354444530539408711613 absolute error = 1e-31 relative error = 2.7405740455860017528387610770351e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -17.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 3.6601070704704444233286209516646 y[1] (numeric) = 3.6601070704704444233286209516644 absolute error = 2e-31 relative error = 5.4643210198299856427270092053541e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = -17.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 3.6711775542628152190005762467649 y[1] (numeric) = 3.6711775542628152190005762467647 absolute error = 2e-31 relative error = 5.4478432885319999624958599698602e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 3.6820809216924030528847274431343 y[1] (numeric) = 3.6820809216924030528847274431341 absolute error = 2e-31 relative error = 5.4317111506629668166635455740972e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = -17.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 3.6928160824315510754352649891385 y[1] (numeric) = 3.6928160824315510754352649891383 absolute error = 2e-31 relative error = 5.4159209539704212888665811435832e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4342 Order of pole (three term test) = -18.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 3.7033819629731313093127194908166 y[1] (numeric) = 3.7033819629731313093127194908165 absolute error = 1e-31 relative error = 2.7002345693696277710762006575522e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = -18.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 3.7137775067378944675954043032904 y[1] (numeric) = 3.7137775067378944675954043032903 absolute error = 1e-31 relative error = 2.6926761180111173815411995474675e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4255 Order of pole (three term test) = -18.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 3.7240016741801269982283348974453 y[1] (numeric) = 3.7240016741801269982283348974452 absolute error = 1e-31 relative error = 2.6852834329623633664962233640851e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4209 Order of pole (three term test) = -18.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 3.7340534428916047890932273534967 y[1] (numeric) = 3.7340534428916047890932273534966 absolute error = 1e-31 relative error = 2.6780548679710710616719026487072e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4161 Order of pole (three term test) = -19.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 3.7439318077038331384156967803899 y[1] (numeric) = 3.7439318077038331384156967803898 absolute error = 1e-31 relative error = 2.6709888196743188053412604810374e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4112 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 3.753635780788562766597814632532 y[1] (numeric) = 3.7536357807885627665978146325319 absolute error = 1e-31 relative error = 2.6640837268178434632068390893046e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4061 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 3.7631643917565718179586047321076 y[1] (numeric) = 3.7631643917565718179586047321075 absolute error = 1e-31 relative error = 2.6573380694995880412039346241472e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 3.7725166877547039742646220077652 y[1] (numeric) = 3.7725166877547039742646220077651 absolute error = 1e-31 relative error = 2.6507503684368641633412839992689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3954 Order of pole (three term test) = -19.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 3.7816917335611529763201257168595 y[1] (numeric) = 3.7816917335611529763201257168594 absolute error = 1e-31 relative error = 2.6443191842565059808945709079016e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3898 Order of pole (three term test) = -20.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 3.7906886116789840252440916372413 y[1] (numeric) = 3.7906886116789840252440916372412 absolute error = 1e-31 relative error = 2.6380431168074150382337041622013e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = -20.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 3.7995064224278827113718697686577 y[1] (numeric) = 3.7995064224278827113718697686576 absolute error = 1e-31 relative error = 2.6319208044949177848913455032412e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3782 Order of pole (three term test) = -20.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 3.8081442840341222959650545638867 y[1] (numeric) = 3.8081442840341222959650545638865 absolute error = 2e-31 relative error = 5.2519018472727576544702007858731e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3722 Order of pole (three term test) = -20.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 3.8166013327187403490763691874322 y[1] (numeric) = 3.816601332718740349076369187432 absolute error = 2e-31 relative error = 5.2402643756750673778192875791742e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.366 Order of pole (three term test) = -20.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 3.8248767227839159259792575999741 y[1] (numeric) = 3.824876722783915925979257599974 absolute error = 1e-31 relative error = 2.6144633473890248283125458504858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3596 Order of pole (three term test) = -21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 3.8329696266975386445165222497856 y[1] (numeric) = 3.8329696266975386445165222497854 absolute error = 2e-31 relative error = 5.2178863773652879473904263967015e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3532 Order of pole (three term test) = -21.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 3.8408792351759612065307465035586 y[1] (numeric) = 3.8408792351759612065307465035584 absolute error = 2e-31 relative error = 5.2071410672936050214615035115348e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3465 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 3.8486047572649270881933189790534 y[1] (numeric) = 3.8486047572649270881933189790533 absolute error = 1e-31 relative error = 2.5983442392007697210734012962417e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3398 Order of pole (three term test) = -21.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 3.8561454204186653065304663942802 y[1] (numeric) = 3.8561454204186653065304663942801 absolute error = 1e-31 relative error = 2.5932631967272361499344115765650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3329 Order of pole (three term test) = -21.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=128057788, alloc=4586680, time=5.04 x[1] = 2.77 y[1] (analytic) = 3.8635004705771443527355544156581 y[1] (numeric) = 3.863500470577144352735554415658 absolute error = 1e-31 relative error = 2.5883263315627763013321982233126e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3258 Order of pole (three term test) = -21.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 3.8706691722414775669387033382352 y[1] (numeric) = 3.870669172241477566938703338235 absolute error = 2e-31 relative error = 5.1670652050116024914774519179122e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3187 Order of pole (three term test) = -22.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 3.8776508085474724139590792392482 y[1] (numeric) = 3.877650808547472413959079239248 absolute error = 2e-31 relative error = 5.1577620026832151993415404109440e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = -22.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 3.8844446813373163051735762347323 y[1] (numeric) = 3.8844446813373163051735762347321 absolute error = 2e-31 relative error = 5.1487411047682894455523444815608e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.304 Order of pole (three term test) = -22.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 3.8910501112293917979794409567177 y[1] (numeric) = 3.8910501112293917979794409567175 absolute error = 2e-31 relative error = 5.1400006240682737933594117351850e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2965 Order of pole (three term test) = -22.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 3.8974664376862141913890721275201 y[1] (numeric) = 3.8974664376862141913890721275199 absolute error = 2e-31 relative error = 5.1315387367064234439767417907712e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2888 Order of pole (three term test) = -22.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 3.9036930190804847240540502254491 y[1] (numeric) = 3.9036930190804847240540502254489 absolute error = 2e-31 relative error = 5.1233536813074000306602160941704e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.281 Order of pole (three term test) = -22.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 3.9097292327592527694536389871725 y[1] (numeric) = 3.9097292327592527694536389871723 absolute error = 2e-31 relative error = 5.1154437582075722525627241608078e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2732 Order of pole (three term test) = -22.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 3.9155744751061806120817082143499 y[1] (numeric) = 3.9155744751061806120817082143497 absolute error = 2e-31 relative error = 5.1078073286954016859668305175902e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2652 Order of pole (three term test) = -23.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 3.9212281616019045782063463327855 y[1] (numeric) = 3.9212281616019045782063463327854 absolute error = 1e-31 relative error = 2.5502214071406619329341812450230e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = -23.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 3.9266897268824864851393875174759 y[1] (numeric) = 3.9266897268824864851393875174757 absolute error = 2e-31 relative error = 5.0933486959965597780161134022414e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2489 Order of pole (three term test) = -23.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 3.931958624795949563919635809531 y[1] (numeric) = 3.9319586247959495639196358095309 absolute error = 1e-31 relative error = 2.5432617568601586367287444519065e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2406 Order of pole (three term test) = -23.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 3.9370343284568932018646310144186 y[1] (numeric) = 3.9370343284568932018646310144184 absolute error = 2e-31 relative error = 5.0799658655348656462953613388534e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2322 Order of pole (three term test) = -23.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 3.9419163302991810435622133386911 y[1] (numeric) = 3.9419163302991810435622133386909 absolute error = 2e-31 relative error = 5.0736744071079897315290143640964e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2237 Order of pole (three term test) = -23.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 3.9466041421266971815356942132055 y[1] (numeric) = 3.9466041421266971815356942132053 absolute error = 2e-31 relative error = 5.0676478511023524132940299788416e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2151 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 3.9510972951621653610058634703165 y[1] (numeric) = 3.9510972951621653610058634703163 absolute error = 2e-31 relative error = 5.0618849666113164133102732705303e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2065 Order of pole (three term test) = -23.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 3.9553953400940263168700392093527 y[1] (numeric) = 3.9553953400940263168700392093524 absolute error = 3e-31 relative error = 7.5845768679311965241104652229065e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 3.9594978471213685552035267626566 y[1] (numeric) = 3.9594978471213685552035267626564 absolute error = 2e-31 relative error = 5.0511455674967436749183871820173e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1889 Order of pole (three term test) = -24.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 3.9634044059969080862427788094039 y[1] (numeric) = 3.9634044059969080862427788094037 absolute error = 2e-31 relative error = 5.0461668684978502576660713026906e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.18 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 3.9671146260680128109127746459523 y[1] (numeric) = 3.9671146260680128109127746459521 absolute error = 2e-31 relative error = 5.0414474713131510575129252078004e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1711 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 3.9706281363157674584941527496123 y[1] (numeric) = 3.9706281363157674584941527496121 absolute error = 2e-31 relative error = 5.0369864196241326386968728295454e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.162 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 3.9739445853920751689688839287908 y[1] (numeric) = 3.9739445853920751689688839287906 absolute error = 2e-31 relative error = 5.0327828106910481312397597827789e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1529 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 3.9770636416547920099171683744217 y[1] (numeric) = 3.9770636416547920099171683744215 absolute error = 2e-31 relative error = 5.0288357949631207579342572875621e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 3.9799849932008909145431455894625 y[1] (numeric) = 3.9799849932008909145431455894623 absolute error = 2e-31 relative error = 5.0251445757123471923788782132044e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1345 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 3.9827083478976517244632511483648 y[1] (numeric) = 3.9827083478976517244632511483646 absolute error = 2e-31 relative error = 5.0217084086906288313225684109678e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1253 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=132058596, alloc=4586680, time=5.20 x[1] = 3.02 y[1] (analytic) = 3.9852334334118742182789330665261 y[1] (numeric) = 3.9852334334118742182789330665258 absolute error = 3e-31 relative error = 7.5277899027149653590821985970483e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1159 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 3.9875599972371112046552146174169 y[1] (numeric) = 3.9875599972371112046552146174166 absolute error = 3e-31 relative error = 7.5233977722683323656376568140899e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1066 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 3.9896878067189189566184899096864 y[1] (numeric) = 3.9896878067189189566184899096861 absolute error = 3e-31 relative error = 7.5193853387420086617823010737279e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09716 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 3.9916166490781224620511644031298 y[1] (numeric) = 3.9916166490781224620511644031296 absolute error = 2e-31 relative error = 5.0105011974581949165390051382900e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08771 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 3.9933463314320931638774785435863 y[1] (numeric) = 3.9933463314320931638774785435861 absolute error = 2e-31 relative error = 5.0083309435441837806525367102764e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07822 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 3.9948766808140370621842273254535 y[1] (numeric) = 3.9948766808140370621842273254533 absolute error = 2e-31 relative error = 5.0064123621269317351371643491289e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06871 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 3.9962075441902912494822370747196 y[1] (numeric) = 3.9962075441902912494822370747193 absolute error = 3e-31 relative error = 7.5071176029418609223580647888096e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05916 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 3.9973387884756271494694870361715 y[1] (numeric) = 3.9973387884756271494694870361712 absolute error = 3e-31 relative error = 7.5049930935277086471804022180546e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04959 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 3.9982703005465589289847521090829 y[1] (numeric) = 3.9982703005465589289847521090826 absolute error = 3e-31 relative error = 7.5032445895163802890573184149859e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04001 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 3.9990019872526557523216616734337 y[1] (numeric) = 3.9990019872526557523216616734333 absolute error = 4e-31 relative error = 1.0002495654542122120557853183483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0304 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 3.9995337754258567466871699479512 y[1] (numeric) = 3.9995337754258567466871699479508 absolute error = 4e-31 relative error = 1.0001165697304540480613035180140e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02079 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 3.9998656118877877473156544782784 y[1] (numeric) = 3.999865611887787747315654478278 absolute error = 4e-31 relative error = 1.0000335981568512814348053266517e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01116 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 3.9999974634550790905702286126901 y[1] (numeric) = 3.9999974634550790905702286126897 absolute error = 4e-31 relative error = 1.0000006341366323563709343875914e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001534 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 3.9999293169426839232563893135895 y[1] (numeric) = 3.9999293169426839232563893135891 absolute error = 4e-31 relative error = 1.0000176710765904490557758240534e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9996611791651966963198341885479 y[1] (numeric) = 3.9996611791651966963198341885476 absolute error = 3e-31 relative error = 7.5006353428821076199104936946435e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 3.9991930769361717110801767002706 y[1] (numeric) = 3.9991930769361717110801767002703 absolute error = 3e-31 relative error = 7.5015132860210261754651570018446e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 3.9985250570654417861453683077206 y[1] (numeric) = 3.9985250570654417861453683077204 absolute error = 2e-31 relative error = 5.0018443587491742386103345761494e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 3.997657186354437313137901659399 y[1] (numeric) = 3.9976571863544373131379016593987 absolute error = 3e-31 relative error = 7.5043953499568940465513731113535e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 3.9965895515895061693233214445672 y[1] (numeric) = 3.9965895515895061693233214445669 absolute error = 3e-31 relative error = 7.5064000475276553768314583301541e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 3.9953222595332351551442133304085 y[1] (numeric) = 3.9953222595332351551442133304082 absolute error = 3e-31 relative error = 7.5087810322226260200501242469929e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 3.9938554369137738245086854749517 y[1] (numeric) = 3.9938554369137738245086854749514 absolute error = 3e-31 relative error = 7.5115387809785893512646122912770e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 3.9921892304121617754414169891699 y[1] (numeric) = 3.9921892304121617754414169891696 absolute error = 3e-31 relative error = 7.5146738464856633776273392647560e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 3.9903238066476606683576476874849 y[1] (numeric) = 3.9903238066476606683576476874847 absolute error = 2e-31 relative error = 5.0121245716152400014165379387955e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 3.9882593521610924387460584503432 y[1] (numeric) = 3.988259352161092438746058450343 absolute error = 2e-31 relative error = 5.0147190124841627111547735416959e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 3.9859960733961853704253891343433 y[1] (numeric) = 3.9859960733961853704253891343431 absolute error = 2e-31 relative error = 5.0175664079265924540316559927987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=136060212, alloc=4586680, time=5.35 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 3.9835341966789298947519234809895 y[1] (numeric) = 3.9835341966789298947519234809893 absolute error = 2e-31 relative error = 5.0206673301998984165173116825552e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 3.9808739681949461801807168322634 y[1] (numeric) = 3.9808739681949461801807168322632 absolute error = 2e-31 relative error = 5.0240224030675934283633736393246e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 3.978015653964865775402750251079 y[1] (numeric) = 3.9780156539648657754027502510787 absolute error = 3e-31 relative error = 7.5414484530997682553965608269443e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 3.9749595398177297678731821022057 y[1] (numeric) = 3.9749595398177297678731821022054 absolute error = 3e-31 relative error = 7.5472466321948118233093997661825e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 3.9717059313624061178926761411711 y[1] (numeric) = 3.9717059313624061178926761411708 absolute error = 3e-31 relative error = 7.5534293118496720361333851579534e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 3.9682551539570290264845791694624 y[1] (numeric) = 3.9682551539570290264845791694621 absolute error = 3e-31 relative error = 7.5599977410940598157688914953730e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 3.9646075526764633931056934297185 y[1] (numeric) = 3.9646075526764633931056934297182 absolute error = 3e-31 relative error = 7.5669532485623518103022979564216e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 3.9607634922777976167177598021398 y[1] (numeric) = 3.9607634922777976167177598021395 absolute error = 3e-31 relative error = 7.5742972430669632817258099947780e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 3.9567233571638681909107887505431 y[1] (numeric) = 3.9567233571638681909107887505427 absolute error = 4e-31 relative error = 1.0109374952276552352187001787664e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9524875513448197405883306155566 y[1] (numeric) = 3.9524875513448197405883306155563 absolute error = 3e-31 relative error = 7.5901567330155429310033542184499e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 3.9480564983977043441789835319417 y[1] (numeric) = 3.9480564983977043441789835319414 absolute error = 3e-31 relative error = 7.5986754526373481908768577600168e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 3.9434306414241241814082506999811 y[1] (numeric) = 3.9434306414241241814082506999808 absolute error = 3e-31 relative error = 7.6075891090519721649221239695131e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 3.938610443005921742330672149345 y[1] (numeric) = 3.9386104430059217423306721493446 absolute error = 4e-31 relative error = 1.0155866029104483227571337831589e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9335963851589220285644030795314 y[1] (numeric) = 3.933596385158922028564403079531 absolute error = 4e-31 relative error = 1.0168811459893578241303158859441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9283889692847313724695672819059 y[1] (numeric) = 3.9283889692847313724695672819055 absolute error = 4e-31 relative error = 1.0182291089999438974358807571251e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9229887161205976943483002912028 y[1] (numeric) = 3.9229887161205976943483002912024 absolute error = 4e-31 relative error = 1.0196307686440551261108806491260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9173961656873372115989792824511 y[1] (numeric) = 3.9173961656873372115989792824507 absolute error = 4e-31 relative error = 1.0210864132242211739472769646565e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.911611877235332807110330025945 y[1] (numeric) = 3.9116118772353328071103300259446 absolute error = 4e-31 relative error = 1.0225963427708831277063255615682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.9056364291886094570135702798955 y[1] (numeric) = 3.9056364291886094570135702798951 absolute error = 4e-31 relative error = 1.0241608691751665281720787773777e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.8994704190869923102032107515641 y[1] (numeric) = 3.8994704190869923102032107515637 absolute error = 4e-31 relative error = 1.0257803163272989558538584617865e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.8931144635263532037703601070534 y[1] (numeric) = 3.893114463526353203770360107053 absolute error = 4e-31 relative error = 1.0274550202607787436009427328340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 3.8865691980969515896471962947646 y[1] (numeric) = 3.8865691980969515896471962947642 absolute error = 4e-31 relative error = 1.0291853293024062211184535105731e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 3.8798352773198760383185573455335 y[1] (numeric) = 3.8798352773198760383185573455332 absolute error = 3e-31 relative error = 7.7322870317122039655999403418772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 3.8729133745815926753973152533435 y[1] (numeric) = 3.8729133745815926753973152533432 absolute error = 3e-31 relative error = 7.7461066381948260731688050432408e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 3.8658041820666070961653326115152 y[1] (numeric) = 3.8658041820666070961653326115148 absolute error = 4e-31 relative error = 1.0347135580627505085912137150576e-29 % Correct digits = 31 h = 0.01 bytes used=140061176, alloc=4586680, time=5.51 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.8585084106882464918324330245445 y[1] (numeric) = 3.8585084106882464918324330245441 absolute error = 4e-31 relative error = 1.0366700222603675740054825400097e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 3.851026790017568909243078029368 y[1] (numeric) = 3.8510267900175689092430780293677 absolute error = 3e-31 relative error = 7.7901301745717369860133290704960e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 3.8433600682104067530455377722595 y[1] (numeric) = 3.8433600682104067530455377722592 absolute error = 3e-31 relative error = 7.8056699001842349216386114073820e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 3.8355090119325518259125416454209 y[1] (numeric) = 3.8355090119325518259125416454206 absolute error = 3e-31 relative error = 7.8216476370327339101747732024105e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 3.8274744062830893882470412262073 y[1] (numeric) = 3.827474406283089388247041226207 absolute error = 3e-31 relative error = 7.8380667812573026699566164748626e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 3.8192570547158889039032268720735 y[1] (numeric) = 3.8192570547158889039032268720732 absolute error = 3e-31 relative error = 7.8549308334606645136795719277057e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 3.810857778959259322782801709098 y[1] (numeric) = 3.8108577789592593227828017090978 absolute error = 2e-31 relative error = 5.2481622668852197238869066720920e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 3.8022774189337769347112996786957 y[1] (numeric) = 3.8022774189337769347112996786954 absolute error = 3e-31 relative error = 7.8900081963016019815339154370611e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 3.7935168326682940117405834505319 y[1] (numeric) = 3.7935168326682940117405834505316 absolute error = 3e-31 relative error = 7.9082290453153254614431658948879e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 3.7845768962141366379432993870768 y[1] (numeric) = 3.7845768962141366379432993870766 absolute error = 2e-31 relative error = 5.2846065883895234011144949020697e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 3.775458503557500306844808544136 y[1] (numeric) = 3.7754585035575003068448085441358 absolute error = 2e-31 relative error = 5.2973698376381584321829567878835e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 3.766162566530052046859847088796 y[1] (numeric) = 3.7661625665300520468598470887958 absolute error = 2e-31 relative error = 5.3104452202197337759013344406152e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 3.7566900147177480144468744882682 y[1] (numeric) = 3.756690014717748014446874488268 absolute error = 2e-31 relative error = 5.3238355897465932296158246825700e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 3.7470417953678756731448089490565 y[1] (numeric) = 3.7470417953678756731448089490564 absolute error = 1e-31 relative error = 2.6687719396036850787911526187058e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 3.7372188732943298541967818403199 y[1] (numeric) = 3.7372188732943298541967818403197 absolute error = 2e-31 relative error = 5.3515731023722870589964895782512e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 3.7272222307811321710759123729596 y[1] (numeric) = 3.7272222307811321710759123729595 absolute error = 1e-31 relative error = 2.6829631776220252764878413694650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 3.7170528674842034358912497370723 y[1] (numeric) = 3.7170528674842034358912497370722 absolute error = 1e-31 relative error = 2.6903034087777869224155574042177e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 3.7067118003313989003503860567443 y[1] (numeric) = 3.7067118003313989003503860567442 absolute error = 1e-31 relative error = 2.6978088771579028897672490323384e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 3.6962000634208163176713402127088 y[1] (numeric) = 3.6962000634208163176713402127087 absolute error = 1e-31 relative error = 2.7054812587024971703172639057409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 3.6855187079173869945527783452195 y[1] (numeric) = 3.6855187079173869945527783452194 absolute error = 1e-31 relative error = 2.7133222736103814963377584601765e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 3.6746688019477601740112001789793 y[1] (numeric) = 3.6746688019477601740112001789792 absolute error = 1e-31 relative error = 2.7213336871882153362773104072683e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 3.6636514304934912605592113958433 y[1] (numeric) = 3.6636514304934912605592113958431 absolute error = 2e-31 relative error = 5.4590346214530605940376679683122e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 3.6524676952825445688133547124051 y[1] (numeric) = 3.6524676952825445688133547124049 absolute error = 2e-31 relative error = 5.4757500048067794275076109914291e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 3.6411187146791214451662248045814 y[1] (numeric) = 3.6411187146791214451662248045813 absolute error = 1e-31 relative error = 2.7464086682164834728384455873944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=144063072, alloc=4586680, time=5.67 x[1] = 3.76 y[1] (analytic) = 3.6296056235718247796188902751262 y[1] (numeric) = 3.6296056235718247796188902751261 absolute error = 1e-31 relative error = 2.7551202629444884907316082924142e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 3.6179295732601710912292434923924 y[1] (numeric) = 3.6179295732601710912292434923923 absolute error = 1e-31 relative error = 2.7640117911385568135073772000287e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 3.6060917313394615358731605184754 y[1] (numeric) = 3.6060917313394615358731605184753 absolute error = 1e-31 relative error = 2.7730853081448260591099923792344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 3.5940932815840233491217545036803 y[1] (numeric) = 3.5940932815840233491217545036802 absolute error = 1e-31 relative error = 2.7823429211588809535908048689729e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 3.5819354238288333999931363487015 y[1] (numeric) = 3.5819354238288333999931363487013 absolute error = 2e-31 relative error = 5.5835735806262601415574672630399e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 3.5696193738495356931246607487299 y[1] (numeric) = 3.5696193738495356931246607487298 absolute error = 1e-31 relative error = 2.8014191297980986326953936334332e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed 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) = 3.5571463632408648175154553133124 y[1] (numeric) = 3.5571463632408648175154553133123 absolute error = 1e-31 relative error = 2.8112422090186764289555242623877e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed 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) = 3.544517639293487499393045054047 y[1] (numeric) = 3.5445176392934874993930450540469 absolute error = 1e-31 relative error = 2.8212583537863996338841440729793e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed 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) = 3.5317344648692745749461538804954 y[1] (numeric) = 3.5317344648692745749461538804953 absolute error = 1e-31 relative error = 2.8314699475488866098602686370195e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed 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) = 3.5187981182750158556224701479056 y[1] (numeric) = 3.5187981182750158556224701479055 absolute error = 1e-31 relative error = 2.8418794326575907575984933628360e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 3.5057098931345905143996092187297 y[1] (numeric) = 3.5057098931345905143996092187296 absolute error = 1e-31 relative error = 2.8524893116750781854333729379013e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed 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) = 3.4924710982596057758841216186546 y[1] (numeric) = 3.4924710982596057758841216186545 absolute error = 1e-31 relative error = 2.8633021487230845006952928139537e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 3.4790830575185168462617361540826 y[1] (numeric) = 3.4790830575185168462617361540825 absolute error = 1e-31 relative error = 2.8743205708726534614737939116942e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 3.4655471097042411709967766052634 y[1] (numeric) = 3.4655471097042411709967766052633 absolute error = 1e-31 relative error = 2.8855472695777106551824517790954e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed 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) = 3.4518646084002802587446609692287 y[1] (numeric) = 3.4518646084002802587446609692286 absolute error = 1e-31 relative error = 2.8969850021534778845412362295161e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 3.4380369218453624591835272277488 y[1] (numeric) = 3.4380369218453624591835272277487 absolute error = 1e-31 relative error = 2.9086365933011886397411117951715e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 3.4240654327966202303744051685852 y[1] (numeric) = 3.4240654327966202303744051685851 absolute error = 1e-31 relative error = 2.9205049366806220204649101186751e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed 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) = 3.4099515383913155778091796790539 y[1] (numeric) = 3.4099515383913155778091796790538 absolute error = 1e-31 relative error = 2.9325929965320318511467696692693e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 3.3956966500071274924872122988712 y[1] (numeric) = 3.3956966500071274924872122988711 absolute error = 1e-31 relative error = 2.9449038093491096209148427145464e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 3.3813021931210153591603866232805 y[1] (numeric) = 3.3813021931210153591603866232804 absolute error = 1e-31 relative error = 2.9574404856046843954592025702338e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 3.366769607166672448288139617503 y[1] (numeric) = 3.366769607166672448288139617503 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed 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) = 3.3521003453905837462344949786387 y[1] (numeric) = 3.3521003453905837462344949786387 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed 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) = 3.3372958747067025178041274333497 y[1] (numeric) = 3.3372958747067025178041274333497 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed 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) = 3.3223576755497601333401019040203 y[1] (numeric) = 3.3223576755497601333401019040203 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed 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) = 3.3072872417272238292783363661955 y[1] (numeric) = 3.3072872417272238292783363661955 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order 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=148064344, alloc=4586680, time=5.83 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 3.2920860802699172062593648293701 y[1] (numeric) = 3.2920860802699172062593648293701 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed 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) = 3.2767557112813184026231067615307 y[1] (numeric) = 3.2767557112813184026231067615308 absolute error = 1e-31 relative error = 3.0517990601410056604840487493127e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed 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) = 3.2612976677855510133437090437049 y[1] (numeric) = 3.261297667785551013343709043705 absolute error = 1e-31 relative error = 3.0662641128339828781976115592758e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 3.2457134955740829551858931583454 y[1] (numeric) = 3.2457134955740829551858931583455 absolute error = 1e-31 relative error = 3.0809866655316901500461106874257e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 3.2300047530511486080685414569647 y[1] (numeric) = 3.2300047530511486080685414569649 absolute error = 2e-31 relative error = 6.1919413527510963444593853109260e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed 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) = 3.2141730110779096902925716955787 y[1] (numeric) = 3.2141730110779096902925716955788 absolute error = 1e-31 relative error = 3.1112202005101105609856869260315e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed 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) = 3.1982198528153704514157115460792 y[1] (numeric) = 3.1982198528153704514157115460793 absolute error = 1e-31 relative error = 3.1267393926021284324123177287496e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed 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) = 3.1821468735660628911239820364958 y[1] (numeric) = 3.1821468735660628911239820364959 absolute error = 1e-31 relative error = 3.1425325094418195203946707540015e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed 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) = 3.1659556806145178354460742272886 y[1] (numeric) = 3.1659556806145178354460742272886 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 3.1496478930665378230700573593196 y[1] (numeric) = 3.1496478930665378230700573593196 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 3.1332251416872878743398479877489 y[1] (numeric) = 3.133225141687287874339847987749 absolute error = 1e-31 relative error = 3.1915995652373875545459926182738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 3.1166890687382203337196165455186 y[1] (numeric) = 3.1166890687382203337196165455186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 3.100041327812850093105989384141 y[1] (numeric) = 3.100041327812850093105989384141 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 3.0832835836713966183288615471946 y[1] (numeric) = 3.0832835836713966183288615471946 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 3.0664175120743093145003723433254 y[1] (numeric) = 3.0664175120743093145003723433254 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 3.0494447996146928775367804214184 y[1] (numeric) = 3.0494447996146928775367804214184 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 3.0323671435496493891784410855156 y[1] (numeric) = 3.0323671435496493891784410855155 absolute error = 1e-31 relative error = 3.2977537107509120927131822853741e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 3.0151862516305540211578360660934 y[1] (numeric) = 3.0151862516305540211578360660934 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 2.9979038419322813208038025029849 y[1] (numeric) = 2.9979038419322813208038025029848 absolute error = 1e-31 relative error = 3.3356640263533465134092578897236e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 2.9805216426813991553110897627543 y[1] (numeric) = 2.9805216426813991553110897627542 absolute error = 1e-31 relative error = 3.3551173918011180954401442753502e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 2.9630413920833474951376458989737 y[1] (numeric) = 2.9630413920833474951376458989736 absolute error = 1e-31 relative error = 3.3749106666946992313962498559020e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 2.9454648381486193185072768263104 y[1] (numeric) = 2.9454648381486193185072768263103 absolute error = 1e-31 relative error = 3.3950498646201900451347112316034e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 2.9277937385179610187823791790897 y[1] (numeric) = 2.9277937385179610187823791790896 absolute error = 1e-31 relative error = 3.4155411525205204960880784747755e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 2.9100298602866097945203437394119 y[1] (numeric) = 2.9100298602866097945203437394118 absolute error = 1e-31 relative error = 3.4363908551148326440622672861197e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 2.8921749798275855983281554410897 y[1] (numeric) = 2.8921749798275855983281554410896 absolute error = 1e-31 relative error = 3.4576054594719372672645682229952e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=152065500, alloc=4586680, time=5.98 x[1] = 4.26 y[1] (analytic) = 2.874230882614055315173048270972 y[1] (numeric) = 2.8742308826140553151730482709719 absolute error = 1e-31 relative error = 3.4791916197439228173287427509077e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 2.8561993630407869335833546441886 y[1] (numeric) = 2.8561993630407869335833546441885 absolute error = 1e-31 relative error = 3.5011561620662677026697629336598e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 2.8380822242447115641736414736721 y[1] (numeric) = 2.838082224244711564173641473672 absolute error = 1e-31 relative error = 3.5235060896310935470032471212809e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 2.8198812779246112491427492675585 y[1] (numeric) = 2.8198812779246112491427492675584 absolute error = 1e-31 relative error = 3.5462485879404981287563707948899e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 2.8015983441599505938135247926721 y[1] (numeric) = 2.801598344159950593813524792672 absolute error = 1e-31 relative error = 3.5693910302472229706455336380633e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 2.7832352512288703369001201936885 y[1] (numeric) = 2.7832352512288703369001201936884 absolute error = 1e-31 relative error = 3.5929409831902428670105256687859e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 2.7647938354253610599941603188602 y[1] (numeric) = 2.7647938354253610599941603188601 absolute error = 1e-31 relative error = 3.6169062126332139117688940876409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 2.7462759408756353187464749013257 y[1] (numeric) = 2.7462759408756353187464749013257 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 2.7276834193537165583782547088473 y[1] (numeric) = 2.7276834193537165583782547088473 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 2.7090181300962632544764051548717 y[1] (numeric) = 2.7090181300962632544764051548717 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 2.6902819396166467965047051339269 y[1] (numeric) = 2.6902819396166467965047051339268 absolute error = 1e-31 relative error = 3.7170825305488076449497641324066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 2.6714767215183017060874853848457 y[1] (numeric) = 2.6714767215183017060874853848456 absolute error = 1e-31 relative error = 3.7432480393527891628200396906084e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 2.6526043563073668548884570476882 y[1] (numeric) = 2.6526043563073668548884570476881 absolute error = 1e-31 relative error = 3.7698799582463114427332273735060e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 2.6336667312046364178067707335115 y[1] (numeric) = 2.6336667312046364178067707335114 absolute error = 1e-31 relative error = 3.7969876300278928696899242934907e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 2.6146657399568393662382794844354 y[1] (numeric) = 2.6146657399568393662382794844353 absolute error = 1e-31 relative error = 3.8245806518140522714789189995086e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 2.5956032826472663732954129329813 y[1] (numeric) = 2.5956032826472663732954129329811 absolute error = 2e-31 relative error = 7.7053377662559890263766848497259e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 2.5764812655057630681373302869864 y[1] (numeric) = 2.5764812655057630681373302869863 absolute error = 1e-31 relative error = 3.8812624542942293791024037924885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 2.5573016007181086399265806978673 y[1] (numeric) = 2.5573016007181086399265806978672 absolute error = 1e-31 relative error = 3.9103717751523434869543981799336e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 2.5380662062347988533930247123268 y[1] (numeric) = 2.5380662062347988533930247123267 absolute error = 1e-31 relative error = 3.9400075441037926755660692309145e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 2.5187770055792525975441134594889 y[1] (numeric) = 2.5187770055792525975441134594888 absolute error = 1e-31 relative error = 3.9701807575062654200683556442469e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 2.4994359276554611467068272022253 y[1] (numeric) = 2.4994359276554611467068272022252 absolute error = 1e-31 relative error = 4.0009027194308885020917627543848e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 2.4800449065550993688148773106603 y[1] (numeric) = 2.4800449065550993688148773106602 absolute error = 1e-31 relative error = 4.0321850517983066806621672466604e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 2.4606058813641181696596028136977 y[1] (numeric) = 2.4606058813641181696596028136976 absolute error = 1e-31 relative error = 4.0640397049104709106496876647709e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 2.4411207959688375136989640130322 y[1] (numeric) = 2.4411207959688375136989640130321 absolute error = 1e-31 relative error = 4.0964789683958173406733440034490e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 2.4215915988615594119609636495877 y[1] (numeric) = 2.4215915988615594119609636495876 absolute error = 1e-31 relative error = 4.1295154825864146680687126966162e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=156066596, alloc=4586680, time=6.14 x[1] = 4.51 y[1] (analytic) = 2.4020202429457203155807166434815 y[1] (numeric) = 2.4020202429457203155807166434815 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 2.3824086853406023995694422363978 y[1] (numeric) = 2.3824086853406023995694422363977 absolute error = 1e-31 relative error = 4.1974326493736503347208933691486e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 2.3627588871856232655242615827628 y[1] (numeric) = 2.3627588871856232655242615827627 absolute error = 1e-31 relative error = 4.2323404449919985194791392336668e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 2.3430728134442236341454384391956 y[1] (numeric) = 2.3430728134442236341454384391955 absolute error = 1e-31 relative error = 4.2678998034638106823258605856865e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 2.3233524327073726386283848500159 y[1] (numeric) = 2.3233524327073726386283848500158 absolute error = 1e-31 relative error = 4.3041253058396865402557992080671e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 2.3035997169967103682373475852198 y[1] (numeric) = 2.3035997169967103682373475852197 absolute error = 1e-31 relative error = 4.3410319623746856002179814072745e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 2.2838166415673473476423706287492 y[1] (numeric) = 2.2838166415673473476423706287491 absolute error = 1e-31 relative error = 4.3786352275361115198056476191367e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 2.2640051847103406719072668013646 y[1] (numeric) = 2.2640051847103406719072668013645 absolute error = 1e-31 relative error = 4.4169510156309165269893879563386e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 2.244167327554866549350497048793 y[1] (numeric) = 2.2441673275548665493504970487929 absolute error = 1e-31 relative error = 4.4559957170820698935084701819744e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 2.2243050538701090348598156424584 y[1] (numeric) = 2.2243050538701090348598156424583 absolute error = 1e-31 relative error = 4.4957862153848084591819074827995e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 2.2044203498668847646222576563454 y[1] (numeric) = 2.2044203498668847646222576563453 absolute error = 1e-31 relative error = 4.5363399047753555505771014786574e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 2.1845152039990235296306835512316 y[1] (numeric) = 2.1845152039990235296306835512316 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 2.1645916067645245497440145748052 y[1] (numeric) = 2.1645916067645245497440145748052 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 2.1446515505065083325080504015202 y[1] (numeric) = 2.1446515505065083325080504015202 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 2.1246970292139840213851140323542 y[1] (numeric) = 2.1246970292139840213851140323541 absolute error = 1e-31 relative error = 4.7065533873784471599150664009714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 2.1047300383224521564916743335919 y[1] (numeric) = 2.1047300383224521564916743335919 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 2.0847525745143627874017086402106 y[1] (numeric) = 2.0847525745143627874017086402105 absolute error = 1e-31 relative error = 4.7967322943968406903304045188291e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 2.0647666355194488920382407358891 y[1] (numeric) = 2.0647666355194488920382407358891 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 2.044774219914955068144776792884 y[1] (numeric) = 2.044774219914955068144776792884 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 2.0247773269257814743010165926542 y[1] (numeric) = 2.0247773269257814743010165926542 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 2.0047779562245630059221922954494 y[1] (numeric) = 2.0047779562245630059221922954494 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 1.9847781077317036981578346936507 y[1] (numeric) = 1.9847781077317036981578346936507 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007339 Order of pole (three term test) = -0.8943 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 1.9647797814153863520830396301143 y[1] (numeric) = 1.9647797814153863520830396301143 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01698 Order of pole (three term test) = -0.9004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 1.944784977091577383052957365562 y[1] (numeric) = 1.944784977091577383052957365562 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02661 Order of pole (three term test) = -0.9113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 1.9247956942240468905690073752533 y[1] (numeric) = 1.9247956942240468905690073752533 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03623 Order of pole (three term test) = -0.927 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=160067380, alloc=4652204, time=6.29 x[1] = 4.76 y[1] (analytic) = 1.9048139317244239474831825671789 y[1] (numeric) = 1.9048139317244239474831825671789 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04584 Order of pole (three term test) = -0.9476 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 1.8848416877523071028449024544255 y[1] (numeric) = 1.8848416877523071028449024544254 absolute error = 1e-31 relative error = 5.3054853704584079860519453085827e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05543 Order of pole (three term test) = -0.973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 1.8648809595154500871735565706809 y[1] (numeric) = 1.8648809595154500871735565706808 absolute error = 1e-31 relative error = 5.3622725616750833802878716448076e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.065 Order of pole (three term test) = -1.003 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 1.8449337430700427014196995173048 y[1] (numeric) = 1.8449337430700427014196995173047 absolute error = 1e-31 relative error = 5.4202488504327556917303717753508e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07454 Order of pole (three term test) = -1.038 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 1.825002033121106861359569484701 y[1] (numeric) = 1.8250020331211068613595694847009 absolute error = 1e-31 relative error = 5.4794459504782379050358995417346e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08405 Order of pole (three term test) = -1.078 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 1.8050878228230277576521547209232 y[1] (numeric) = 1.8050878228230277576521547209231 absolute error = 1e-31 relative error = 5.5398966596321712233003319840919e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09353 Order of pole (three term test) = -1.122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 1.7851931035802400782765787616605 y[1] (numeric) = 1.7851931035802400782765787616603 absolute error = 2e-31 relative error = 1.1203269808677618361412225977487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -1.172 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 1.7653198648480892245614664220924 y[1] (numeric) = 1.7653198648480892245614664220922 absolute error = 2e-31 relative error = 1.1329391572739740658309354887712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1124 Order of pole (three term test) = -1.226 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 1.7454700939338874345187391805346 y[1] (numeric) = 1.7454700939338874345187391805345 absolute error = 1e-31 relative error = 5.7291156318022636556024786906784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1217 Order of pole (three term test) = -1.284 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 1.7256457757981847077037205630694 y[1] (numeric) = 1.7256457757981847077037205630693 absolute error = 1e-31 relative error = 5.7949320423970405291180884372253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 Order of pole (three term test) = -1.348 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 1.7058488928562744043434585080292 y[1] (numeric) = 1.7058488928562744043434585080291 absolute error = 1e-31 relative error = 5.8621839495150089357840100419421e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1403 Order of pole (three term test) = -1.416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 1.6860814247799533680079404287439 y[1] (numeric) = 1.6860814247799533680079404287438 absolute error = 1e-31 relative error = 5.9309116707131016153521868418806e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = -1.488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 1.6663453482995563956467345059368 y[1] (numeric) = 1.6663453482995563956467345059366 absolute error = 2e-31 relative error = 1.2002313938349729228642100357713e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1586 Order of pole (three term test) = -1.566 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 1.6466426370062848513790828205723 y[1] (numeric) = 1.6466426370062848513790828205722 absolute error = 1e-31 relative error = 6.0729631161383757667052432978067e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1677 Order of pole (three term test) = -1.648 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 1.6269752611548491910113417117562 y[1] (numeric) = 1.626975261154849191011341711756 absolute error = 2e-31 relative error = 1.2292749912991134055521807762218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -1.734 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 1.6073451874664451328648536009612 y[1] (numeric) = 1.607345187466445132864853600961 absolute error = 2e-31 relative error = 1.2442877955496736830573012850513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -1.825 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 1.5877543789320831771329815183765 y[1] (numeric) = 1.5877543789320831771329815183762 absolute error = 3e-31 relative error = 1.8894610147558133039501493106762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = -1.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 1.5682047946162911406514791070285 y[1] (numeric) = 1.5682047946162911406514791070282 absolute error = 3e-31 relative error = 1.9130154494483872407901537504633e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2033 Order of pole (three term test) = -2.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 1.5486983894612093366651383919206 y[1] (numeric) = 1.5486983894612093366651383919203 absolute error = 3e-31 relative error = 1.9371105571070536736444032636851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.212 Order of pole (three term test) = -2.124 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 1.5292371140910979899094851767305 y[1] (numeric) = 1.5292371140910979899094851767303 absolute error = 2e-31 relative error = 1.3078416561899231109043080697272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2206 Order of pole (three term test) = -2.232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 1.5098229146172764361031039541294 y[1] (numeric) = 1.5098229146172764361031039541291 absolute error = 3e-31 relative error = 1.9869879910787200665622309949807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2291 Order of pole (three term test) = -2.345 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 1.4904577324435136117680929719749 y[1] (numeric) = 1.4904577324435136117680929719747 absolute error = 2e-31 relative error = 1.3418696528355240494327011818336e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2375 Order of pole (three term test) = -2.462 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 1.4711435040718892951674933586384 y[1] (numeric) = 1.4711435040718892951674933586382 absolute error = 2e-31 relative error = 1.3594866812546299770732698998444e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2459 Order of pole (three term test) = -2.583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 1.4518821609091455120738168046061 y[1] (numeric) = 1.4518821609091455120738168046059 absolute error = 2e-31 relative error = 1.3775222630655037573794760349050e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2541 Order of pole (three term test) = -2.709 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; 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=163912544, alloc=4652204, time=6.44