|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > array_tmp4[1] := sinh(array_tmp3[1]); > array_tmp4_g[1] := cosh(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[2] := att(1,array_tmp4_g,array_tmp3,1); > array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[3] := att(2,array_tmp4_g,array_tmp3,1); > array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[4] := att(3,array_tmp4_g,array_tmp3,1); > array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[5] := att(4,array_tmp4_g,array_tmp3,1); > array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit sinh FULL $eq_no = 1 > array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1); > array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := sinh(array_tmp3[1]); array_tmp4_g[1] := cosh(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1); array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1); array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1); array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1); array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1); array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2))); > end; exact_soln_y := proc(x) return 20.0*sqrt(0.1*x + 0.2)*cosh(sqrt(0.1*x + 0.2)) - 20.0*sinh(sqrt(0.1*x + 0.2)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sinh_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_g:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T04:53:03-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sinh_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"sinh_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"sinh_sqrt maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sinh_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0\ .1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_g := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2));") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T04:53:03-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sinh_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "sinh_sqrt diffeq.mxt"); logitem_str(html_log_file, "sinh_sqrt maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostode.ode################# diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 4.9 estimated_steps = 4900000 step_error = 2.0408163265306122448979591836735e-17 est_needed_step_err = 2.0408163265306122448979591836735e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.5462659701111932780411530195754e-169 estimated_step_error = 3.5462659701111932780411530195754e-169 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.3798582927465186974489361316836e-161 estimated_step_error = 2.3798582927465186974489361316836e-161 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5970951749065101797331691830308e-153 estimated_step_error = 1.5970951749065101797331691830308e-153 best_h = 8.000e-06 opt_iter = 4 bytes used=4000228, alloc=2948580, time=0.13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0717915025553601229129300822502e-145 estimated_step_error = 1.0717915025553601229129300822502e-145 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 = 7.1926585852669954443628531190167e-138 estimated_step_error = 7.1926585852669954443628531190167e-138 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.8268947809459371493715428449447e-130 estimated_step_error = 4.8268947809459371493715428449447e-130 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 = 3.2392518572551257883930830345708e-122 estimated_step_error = 3.2392518572551257883930830345708e-122 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1737950637693184648635877313750e-114 estimated_step_error = 2.1737950637693184648635877313750e-114 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4587688291722222126800140714695e-106 estimated_step_error = 1.4587688291722222126800140714695e-106 best_h = 0.000512 opt_iter = 10 bytes used=8001508, alloc=3996964, time=0.25 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.7890904560592125644893735450103e-99 estimated_step_error = 9.7890904560592125644893735450103e-99 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 = 6.5686208130714597133797735176637e-91 estimated_step_error = 6.5686208130714597133797735176637e-91 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 = 4.4071519232586872604370313751449e-83 estimated_step_error = 4.4071519232586872604370313751449e-83 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.9562819943962583160531026626434e-75 estimated_step_error = 2.9562819943962583160531026626434e-75 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9821745787971767370965841324634e-67 estimated_step_error = 1.9821745787971767370965841324634e-67 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 = 1.3278687145652528209008124378479e-59 estimated_step_error = 1.3278687145652528209008124378479e-59 best_h = 0.032768 opt_iter = 16 bytes used=12002596, alloc=4193536, time=0.38 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.8798556223201124278833605079654e-52 estimated_step_error = 8.8798556223201124278833605079654e-52 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 = 5.9175855031051205415892212833977e-44 estimated_step_error = 5.9175855031051205415892212833977e-44 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 = 3.9166260729676377302126092675385e-36 estimated_step_error = 3.9166260729676377302126092675385e-36 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.6551348095261795506943912458578 y[1] (numeric) = 0.6551348095261795506943912458578 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 = 2.356 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.15 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.659885502432658648811119586627 y[1] (numeric) = 0.659885502432658648811119586627 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 = 2.367 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.21 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.6646482490656218830436291856422 y[1] (numeric) = 0.66464824906562188304362918564242 absolute error = 2.2e-31 relative error = 3.3100215085089168055518804414317e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.378 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.28 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop bytes used=16003396, alloc=4259060, time=0.51 x[1] = 0.13 y[1] (analytic) = 0.6694230265858070503557101052594 y[1] (numeric) = 0.66942302658580705035571010525969 absolute error = 2.9e-31 relative error = 4.3320888060731747739960227127138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.389 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.34 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.6742098123291202424434289580404 y[1] (numeric) = 0.67420981232912024244342895804123 absolute error = 8.3e-31 relative error = 1.2310707806709132945703371943556e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.401 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.41 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.6790085838045605523196519902016 y[1] (numeric) = 0.67900858380456055231965199020171 absolute error = 1.1e-31 relative error = 1.6200089751981893344516845181123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.412 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.47 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.683819318692178806282425592305 y[1] (numeric) = 0.68381931869217880628242559230519 absolute error = 1.9e-31 relative error = 2.7785117326515380275518106556403e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.423 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.53 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.6886419948410696092005201203024 y[1] (numeric) = 0.688641994841069609200520120302 absolute error = 4.0e-31 relative error = 5.8085333598093338423926837411818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.434 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.6 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.6934765902673960091569874890826 y[1] (numeric) = 0.69347659026739600915698748908274 absolute error = 1.4e-31 relative error = 2.0188136407894854665839599469085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.446 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.66 Order of pole (six term test) = -2.494 bytes used=20004356, alloc=4324584, time=0.65 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.6983230831524461050577889395924 y[1] (numeric) = 0.69832308315244610505778893959221 absolute error = 1.9e-31 relative error = 2.7208036592787583387329813121974e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.457 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.73 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.7031814518407209378559976388712 y[1] (numeric) = 0.70318145184072093785599763887148 absolute error = 2.8e-31 relative error = 3.9819025269657335899752019028240e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.468 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.79 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.7080516748380530225806329675494 y[1] (numeric) = 0.70805167483805302258063296754926 absolute error = 1.4e-31 relative error = 1.9772568157828463083543643496376e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.479 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.85 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.7129337308097548944100127349664 y[1] (numeric) = 0.71293373080975489441001273496567 absolute error = 7.3e-31 relative error = 1.0239380863223586335684355678269e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.92 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0.7178275985787970576091305391966 y[1] (numeric) = 0.71782759857879705760913053919642 absolute error = 1.8e-31 relative error = 2.5075658884720509756596899563873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.502 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.98 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop bytes used=24005688, alloc=4390108, time=0.78 x[1] = 0.24 y[1] (analytic) = 0.722733257124014741274861724926 y[1] (numeric) = 0.72273325712401474127486172492564 absolute error = 3.6e-31 relative error = 4.9810908305583498413464044333270e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.513 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.04 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.7276506855783428805170526185262 y[1] (numeric) = 0.72765068557834288051705261852583 absolute error = 3.7e-31 relative error = 5.0848574368609422843425009999107e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.524 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.1 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.7325798632270787559624552799122 y[1] (numeric) = 0.73257986322707875596245527991269 absolute error = 4.9e-31 relative error = 6.6886905386875757919338009848367e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.535 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.17 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.7375207695061717383161812158466 y[1] (numeric) = 0.73752076950617173831618121584717 absolute error = 5.7e-31 relative error = 7.7285959062774585746970562026149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.546 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.23 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.7424733840005395981654788570112 y[1] (numeric) = 0.74247338400053959816547885701142 absolute error = 2.2e-31 relative error = 2.9630691785153622871242023763033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.558 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.29 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.7474376864424108542762989725972 y[1] (numeric) = 0.74743768644241085427629897259771 absolute error = 5.1e-31 relative error = 6.8233112840142409220802243948089e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.569 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.35 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop bytes used=28006800, alloc=4390108, time=0.92 x[1] = 0.3 y[1] (analytic) = 0.7524136567096926463269199354222 y[1] (numeric) = 0.75241365670969264632691993542249 absolute error = 2.9e-31 relative error = 3.8542628435024815697327064293901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.42 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.757401274824363630357013877376 y[1] (numeric) = 0.75740127482436363035701387737554 absolute error = 4.6e-31 relative error = 6.0733988084014114157672387685164e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.591 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.48 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.762400520950891407196650228742 y[1] (numeric) = 0.76240052095089140719665022874088 absolute error = 1.12e-30 relative error = 1.4690441168679929185743917367430e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.603 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.54 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.767411375394674005789130156026 y[1] (numeric) = 0.76741137539467400578913015602655 absolute error = 5.5e-31 relative error = 7.1669513592646324766077075691469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.614 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.6 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.772433818600504954645087094471 y[1] (numeric) = 0.7724338186005049546450870944713 absolute error = 3.0e-31 relative error = 3.8838278798245756184339128038557e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.625 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.66 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop bytes used=32007820, alloc=4390108, time=1.06 x[1] = 0.35 y[1] (analytic) = 0.777467831151061485673442621704 y[1] (numeric) = 0.77746783115106148567344262170445 absolute error = 4.5e-31 relative error = 5.7880208282542470552393614871273e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.636 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.72 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.782513393765415425337661674216 y[1] (numeric) = 0.78251339376541542533766167421662 absolute error = 6.2e-31 relative error = 7.9231870654199402339069448141104e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.647 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.78 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.787570487297566338493030831048 y[1] (numeric) = 0.78757048729756633849303083104805 absolute error = 5e-32 relative error = 6.3486380973425925328717947393214e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.659 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.85 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0.792639092734996500381762888633 y[1] (numeric) = 0.79263909273499650038176288863245 absolute error = 5.5e-31 relative error = 6.9388452454726684460409558525918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.91 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.797719191197247282106649556635 y[1] (numeric) = 0.79771919119724728210664955663511 absolute error = 1.1e-31 relative error = 1.3789313484474131691124006260990e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.681 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.97 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.802810763934516544479459025773 y[1] (numeric) = 0.80281076393451654447945902577262 absolute error = 3.8e-31 relative error = 4.7333695195820236814834658191690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.692 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.03 Order of pole (six term test) = -2.494 TOP MAIN SOLVE Loop bytes used=36008888, alloc=4390108, time=1.19 x[1] = 0.41 y[1] (analytic) = 0.807913792326276644455714256659 y[1] (numeric) = 0.80791379232627664445571425666 absolute error = 1.00e-30 relative error = 1.2377558218441073274723595704373e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.703 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.09 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0.813028257879912667431001844197 y[1] (numeric) = 0.81302825787991266743100184419683 absolute error = 1.7e-31 relative error = 2.0909482339924972152198139066581e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.15 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.818154142229380507493375509347 y[1] (numeric) = 0.81815414222938050749337550934704 absolute error = 4e-32 relative error = 4.8890542668407663590480387559602e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.726 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.21 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.823291427133884426309283677217 y[1] (numeric) = 0.82329142713388442630928367721726 absolute error = 2.6e-31 relative error = 3.1580554762380460865784984662432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.737 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.27 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0.828440094476573729674054665802 y[1] (numeric) = 0.82844009447657372967405466580225 absolute error = 2.5e-31 relative error = 3.0177197080007985026943424026659e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.748 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.33 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0.833600126263258208889349851516 y[1] (numeric) = 0.83360012626325820888934985151573 absolute error = 2.7e-31 relative error = 3.2389630410724246833288887722748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.39 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop bytes used=40009784, alloc=4455632, time=1.33 x[1] = 0.47 y[1] (analytic) = 0.838771504621142002045935383275 y[1] (numeric) = 0.83877150462114200204593538327489 absolute error = 1.1e-31 relative error = 1.3114417859210062333332788011522e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.771 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.45 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.843954211797575537997183027074 y[1] (numeric) = 0.84395421179757553799718302707317 absolute error = 8.3e-31 relative error = 9.8346567668895941300426728210002e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.782 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.51 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0.849148230158825233313221816615 y[1] (numeric) = 0.84914823015882523331322181661435 absolute error = 6.5e-31 relative error = 7.6547294914390103628580835607756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.793 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.57 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.854353542188860619813739085797 y[1] (numeric) = 0.85435354218886061981373908579699 absolute error = 1e-32 relative error = 1.1704756293723462401936906103464e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.804 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.63 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.859570130488158587394978576667 y[1] (numeric) = 0.85957013048815858739497857666623 absolute error = 7.7e-31 relative error = 8.9579659958950550940056717025905e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.816 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.69 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop bytes used=44010700, alloc=4455632, time=1.46 x[1] = 0.52 y[1] (analytic) = 0.864797977772524433799210649202 y[1] (numeric) = 0.86479797777252443379921064920234 absolute error = 3.4e-31 relative error = 3.9315540593161892033146750710655e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.827 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.75 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.870037066871929419728368319301 y[1] (numeric) = 0.87003706687192941972836831929986 absolute error = 1.14e-30 relative error = 1.3102890019372122599480418476381e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.838 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.81 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.875287380729364534282980479894 y[1] (numeric) = 0.87528738072936453428298047989501 absolute error = 1.01e-30 relative error = 1.1539067307909561710928103640936e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.849 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.87 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0.880548902399710182118139141612 y[1] (numeric) = 0.88054890239971018211813914161105 absolute error = 9.5e-31 relative error = 1.0788725048785123288845539637016e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.861 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.92 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.885821615048621509954987817427 y[1] (numeric) = 0.88582161504862150995498781742733 absolute error = 3.3e-31 relative error = 3.7253550194966371573961653913493e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.872 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.98 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.89110550195142909617392464741 y[1] (numeric) = 0.8911055019514290961739246474102 absolute error = 2.0e-31 relative error = 2.2444031549801974960620131678936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.883 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.04 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop bytes used=48011840, alloc=4455632, time=1.60 x[1] = 0.58 y[1] (analytic) = 0.896400546492054733149028445317 y[1] (numeric) = 0.89640054649205473314902844531714 absolute error = 1.4e-31 relative error = 1.5618018144664405692486572313342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.894 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.1 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.901706732161942037766636915383 y[1] (numeric) = 0.90170673216194203776663691538261 absolute error = 3.9e-31 relative error = 4.3251312881398998201006947487123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.905 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.16 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.90702404255900163120888427959 y[1] (numeric) = 0.90702404255900163120888427958951 absolute error = 4.9e-31 relative error = 5.4022823763034445997577723033513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.917 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.22 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0.912352461386570634579548410683 y[1] (numeric) = 0.91235246138657063457954841068358 absolute error = 5.8e-31 relative error = 6.3571922535127530679345486552192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.928 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.28 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.917691972452386232308835910475 y[1] (numeric) = 0.91769197245238623230883591047631 absolute error = 1.31e-30 relative error = 1.4274942348021556643575694828252e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.939 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.33 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.923042559667573060499685709537 y[1] (numeric) = 0.92304255966757306049968570953768 absolute error = 6.8e-31 relative error = 7.3669409159735490660113537324201e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.39 Order of pole (six term test) = -2.493 bytes used=52017388, alloc=4455632, time=1.74 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0.928404207045644182474608460889 y[1] (numeric) = 0.92840420704564418247460846088828 absolute error = 7.2e-31 relative error = 7.7552427545667275122285945551752e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.961 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.45 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.933776898701515418752688086644 y[1] (numeric) = 0.93377689870151541875268808664467 absolute error = 6.7e-31 relative error = 7.1751614430779306082608222385245e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.973 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.51 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.939160618850532803534722619821 y[1] (numeric) = 0.93916061885053280353472261982223 absolute error = 1.23e-30 relative error = 1.3096801285231000695064620545895e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.984 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.57 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0.944555351807512944504028988345 y[1] (numeric) = 0.94455535180751294450402898834539 absolute error = 3.9e-31 relative error = 4.1289268993467785477259895698601e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.995 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.62 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.949961081985796067364525430468 y[1] (numeric) = 0.94996108198579606736452543046826 absolute error = 2.6e-31 relative error = 2.7369542282352947101934344464863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.006 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.68 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop bytes used=56018300, alloc=4455632, time=1.88 x[1] = 0.69 y[1] (analytic) = 0.955377793896311531039574330557 y[1] (numeric) = 0.95537779389631153103957433055795 absolute error = 9.5e-31 relative error = 9.9437102899955492327003665303670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.018 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.74 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.960805472146655603847853406952 y[1] (numeric) = 0.9608054721466556038478534069528 absolute error = 8.0e-31 relative error = 8.3263472491743828414888729417547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.029 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.8 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.966244101440181295259261433989 y[1] (numeric) = 0.96624410144018129525926143398778 absolute error = 1.22e-30 relative error = 1.2626209031254079505535211282943e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.85 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.971693666575100042017497655899 y[1] (numeric) = 0.97169366657510004201749765589917 absolute error = 1.7e-31 relative error = 1.7495225691775266722335966749415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.051 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.91 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.977154152443595051499331261312 y[1] (numeric) = 0.97715415244359505149933126131158 absolute error = 4.2e-31 relative error = 4.2981959289605940860173608461000e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.062 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.97 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.982625544030946109166459346866 y[1] (numeric) = 0.98262554403094610916645934686599 absolute error = 1e-32 relative error = 1.0176816652839901260387115483780e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.074 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.02 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop bytes used=60019184, alloc=4521156, time=2.02 x[1] = 0.75 y[1] (analytic) = 0.988107826414665660856913511735 y[1] (numeric) = 0.98810782641466566085691351173501 absolute error = 1e-32 relative error = 1.0120352994556119564027360561944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.085 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.08 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.993600984763645984461808556263 y[1] (numeric) = 0.99360098476364598446180855626242 absolute error = 5.8e-31 relative error = 5.8373533127885152968047128529178e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.096 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.14 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.999105004337317269242343689612 y[1] (numeric) = 0.99910500433731726924234368961227 absolute error = 2.7e-31 relative error = 2.7024186529731638894178929758361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.107 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.19 Order of pole (six term test) = -2.493 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 1.004619870484816424663801929786 y[1] (numeric) = 1.0046198704848164246638019297854 absolute error = 6e-31 relative error = 5.9724082474144955811553885416151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.118 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.25 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 1.010145568644166444160207160114 y[1] (numeric) = 1.0101455686441664441602071601144 absolute error = 4e-31 relative error = 3.9598253203930439893459590983621e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.31 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 1.015682084341466152697578697938 bytes used=64021180, alloc=4521156, time=2.16 y[1] (numeric) = 1.015682084341466152697578697938 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 = 3.141 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.36 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 1.021229403190090170377588743987 y[1] (numeric) = 1.021229403190090170377588743987 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 = 3.152 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.42 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 1.02678751088989892761902998444 y[1] (numeric) = 1.0267875108898989276190299844405 absolute error = 5e-31 relative error = 4.8695566969514332302336379130278e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.163 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.47 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 1.032356393226458570673925209127 y[1] (numeric) = 1.0323563932264585706739252091263 absolute error = 7e-31 relative error = 6.7806041071946692401399682631755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.175 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.53 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 1.037936036070270599380381599454 y[1] (numeric) = 1.0379360360702705993803815994538 absolute error = 2e-31 relative error = 1.9269010136426128582982051246204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.186 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.59 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 1.043526425376011082127372155861 y[1] (numeric) = 1.0435264253760110821273721558609 absolute error = 1e-31 relative error = 9.5828910095848572129616477908233e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.197 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.64 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop bytes used=68022180, alloc=4521156, time=2.29 x[1] = 0.86 y[1] (analytic) = 1.0491275471817792960094197476 y[1] (numeric) = 1.0491275471817792960094197475997 absolute error = 3e-31 relative error = 2.8595188526492848595841410286331e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.208 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.7 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 1.054739387608355643083512943464 y[1] (numeric) = 1.054739387608355643083512943465 absolute error = 1.0e-30 relative error = 9.4810150426592261095096343425240e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.219 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.75 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 1.060361932858468696508289761856 y[1] (numeric) = 1.060361932858468696508289761856 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 = 3.231 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.81 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 1.065995169216071233148325390654 y[1] (numeric) = 1.0659951692160712331483253906546 absolute error = 6e-31 relative error = 5.6285433304659129292521660955121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.242 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.86 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 1.071639083045625111965941132832 y[1] (numeric) = 1.0716390830456251119659411328319 absolute error = 1e-31 relative error = 9.3314999034747310276045582814810e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.253 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.92 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 1.077293660791394860200953108598 y[1] (numeric) = 1.0772936607913948602009531085976 absolute error = 4e-31 relative error = 3.7130080177595629207175995868011e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.264 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.98 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop bytes used=72023156, alloc=4521156, time=2.43 x[1] = 0.92 y[1] (analytic) = 1.082958888976749831956791402155 y[1] (numeric) = 1.082958888976749831956791402154 absolute error = 1.0e-30 relative error = 9.2339608657246924742980811742885e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.275 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.03 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 1.088634754203474806370987793471 y[1] (numeric) = 1.0886347542034748063709877934721 absolute error = 1.1e-30 relative error = 1.0104399071889275138236254555342e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.287 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.09 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 1.094321243151088895050652482729 y[1] (numeric) = 1.0943212431510888950506524827294 absolute error = 4e-31 relative error = 3.6552338036334133042661166102129e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.298 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.14 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 1.10001834257617263090069337706 y[1] (numeric) = 1.1000183425761726309006933770603 absolute error = 3e-31 relative error = 2.7272272505694694134248574993643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.309 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.19 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 1.105726039311703112865589607517 y[1] (numeric) = 1.1057260393117031128655896075163 absolute error = 7e-31 relative error = 6.3306820596875775441813935001104e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.25 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop bytes used=76024072, alloc=4521156, time=2.57 x[1] = 0.97 y[1] (analytic) = 1.111444320266397083445887333173 y[1] (numeric) = 1.1114443202663970834458873331737 absolute error = 7e-31 relative error = 6.2981112704972944810423330540116e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.332 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.3 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 1.117173172424061818139574540544 y[1] (numeric) = 1.1171731724240618181395745405447 absolute error = 7e-31 relative error = 6.2658146228227786863827768156668e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.343 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.36 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 1.122912582842953708197408305759 y[1] (numeric) = 1.1229125828429537081974083057599 absolute error = 9e-31 relative error = 8.0148714490437817458732588405012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.354 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.41 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 1.128662538655144420271371788332 y[1] (numeric) = 1.1286625386551444202713717883317 absolute error = 3e-31 relative error = 2.6580132654838034857421640875574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.365 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.47 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 1.134423027065894518677952261542 y[1] (numeric) = 1.1344230270658945186779522615408 absolute error = 1.2e-30 relative error = 1.0578064543556698737884503953175e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.376 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.52 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 1.140194035353034438094044337456 y[1] (numeric) = 1.1401940353530344380940443374562 absolute error = 2e-31 relative error = 1.7540874079215356863155155102761e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.388 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.58 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop bytes used=80024956, alloc=4521156, time=2.71 x[1] = 1.03 y[1] (analytic) = 1.145975550866352696554149275769 y[1] (numeric) = 1.1459755508663526965541492757688 absolute error = 2e-31 relative error = 1.7452379315492450182499319342913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.399 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.63 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 1.151767561026991240624284468915 y[1] (numeric) = 1.1517675610269912406242844689148 absolute error = 2e-31 relative error = 1.7364614768423146712010486217299e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.68 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 1.157570053326847816591728014162 y[1] (numeric) = 1.1575700533268478165917280141619 absolute error = 1e-31 relative error = 8.6387860253123114006678078784501e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.421 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.74 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 1.163383015327985263431462389384 y[1] (numeric) = 1.1633830153279852634314623893839 absolute error = 1e-31 relative error = 8.5956214490382282525244433286654e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.433 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.79 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 1.16920643466204762519097979395 y[1] (numeric) = 1.1692064346620476251909797939509 absolute error = 9e-31 relative error = 7.6975286255599491967972260647909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.444 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.85 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 1.175040299029682982275972243257 y[1] (numeric) = 1.1750402990296829822759722432564 absolute error = 6e-31 relative error = 5.1062078508751064739993601658948e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.455 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.9 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop bytes used=84025688, alloc=4521156, time=2.85 x[1] = 1.09 y[1] (analytic) = 1.180884596199972902921326835543 y[1] (numeric) = 1.1808845961999729029213268355441 absolute error = 1.1e-30 relative error = 9.3150507978488714667716264637093e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.466 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.95 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 1.186739314009868417895728694237 y[1] (numeric) = 1.1867393140098684178957286942361 absolute error = 9e-31 relative error = 7.5838053848489592038765414102072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.477 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.01 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 1.192604440363632423214962834842 y[1] (numeric) = 1.1926044403636324232149628348418 absolute error = 2e-31 relative error = 1.6770019734206152281881383807200e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.489 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.06 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 1.198479963232288417329598272226 y[1] (numeric) = 1.1984799632322884173295982722263 absolute error = 3e-31 relative error = 2.5031707596587849053035295816067e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.11 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 1.204365870653075480908005253671 y[1] (numeric) = 1.204365870653075480908005253672 absolute error = 1.0e-30 relative error = 8.3031246929784159759475644338531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.511 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.17 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop bytes used=88026588, alloc=4521156, time=2.98 x[1] = 1.14 y[1] (analytic) = 1.210262150728909408956448024801 y[1] (numeric) = 1.2102621507289094089564480248006 absolute error = 4e-31 relative error = 3.3050690692019940127911434135553e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.522 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.22 Order of pole (six term test) = -2.492 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 1.216168791627849906605136444239 y[1] (numeric) = 1.2161687916278499066051364442398 absolute error = 8e-31 relative error = 6.5780342786891838539866049239620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.533 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.27 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 1.222085781582573761443413175608 y[1] (numeric) = 1.2220857815825737614434131756076 absolute error = 4e-31 relative error = 3.2730926587003487100289861486682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.545 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.33 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 1.228013108889853906809480572261 y[1] (numeric) = 1.2280131088898539068094805722608 absolute error = 2e-31 relative error = 1.6286471093195708843834366076036e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.556 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.38 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 1.233950761910044291930993205106 y[1] (numeric) = 1.2339507619100442919309932051057 absolute error = 3e-31 relative error = 2.4312153228515139859651279153767e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.567 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.43 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 1.239898729066570476273198372237 y[1] (numeric) = 1.2398987290665704762731983722372 absolute error = 2e-31 relative error = 1.6130349625454124441626322498206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.578 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.48 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop bytes used=92027788, alloc=4521156, time=3.12 x[1] = 1.2 y[1] (analytic) = 1.245856998845425866881818216369 y[1] (numeric) = 1.245856998845425866881818216369 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 = 3.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.54 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 1.251825559794673518909234434231 y[1] (numeric) = 1.2518255597946735189092344342322 absolute error = 1.2e-30 relative error = 9.5860001468321669976802605580501e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.601 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.59 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 1.257804400523953420885442559201 y[1] (numeric) = 1.2578044005239534208854425592018 absolute error = 8e-31 relative error = 6.3602894032390923496144929682712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.612 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.64 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 1.26379350970399518764035194767 y[1] (numeric) = 1.2637935097039951876403519476698 absolute error = 2e-31 relative error = 1.5825370083348810441385834061613e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.623 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.69 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 1.269792876066136085101966891807 y[1] (numeric) = 1.2697928760661360851019668918068 absolute error = 2e-31 relative error = 1.5750600256918055792432565097951e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.634 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.75 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 1.27580248840184431248642369911 y[1] (numeric) = 1.2758024884018443124864236991094 absolute error = 6e-31 relative error = 4.7029223210843569174845508127604e-29 % Correct digits = 31 h = 0.01 bytes used=96028976, alloc=4521156, time=3.26 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.646 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.8 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 1.281822335562247468661391595414 y[1] (numeric) = 1.2818223355622474686613915954126 absolute error = 1.4e-30 relative error = 1.0921950422918134767771122774430e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.657 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.85 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 1.287852406457666130704569367806 y[1] (numeric) = 1.2878524064576661307045693678052 absolute error = 8e-31 relative error = 6.2118919527468176703717027500427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.668 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.9 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 1.293892690057152473894506650642 y[1] (numeric) = 1.2938926900571524738945066506422 absolute error = 2e-31 relative error = 1.5457232391595458298213291527204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.679 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.96 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 1.299943175388033863562315445155 y[1] (numeric) = 1.2999431753880338635623154451556 absolute error = 6e-31 relative error = 4.6155863683879844892980447337186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.01 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.306003851535461350400565951727 y[1] (numeric) = 1.3060038515354613504005659517263 absolute error = 7e-31 relative error = 5.3598616817018874364373210106876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.702 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.06 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop bytes used=100030104, alloc=4521156, time=3.40 x[1] = 1.31 y[1] (analytic) = 1.312074707641963001970318934667 y[1] (numeric) = 1.3120747076419630019703189346666 absolute error = 4e-31 relative error = 3.0486068946399613555613785636630e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.713 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.11 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 1.318155732907002004269358643339 y[1] (numeric) = 1.3181557329070020042693586433399 absolute error = 9e-31 relative error = 6.8277213195073699217614034063722e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.724 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.16 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 1.324246916586539468324766348279 y[1] (numeric) = 1.3242469165865394683247663482793 absolute error = 3e-31 relative error = 2.2654385390097679365158327211448e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.735 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.21 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 1.330348247992601877851512325239 y[1] (numeric) = 1.3303482479926018778515123252392 absolute error = 2e-31 relative error = 1.5033657563106905249211408318985e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.747 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.27 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 1.33645971649285311507622845541 y[1] (numeric) = 1.3364597164928531150762284554101 absolute error = 1e-31 relative error = 7.4824552334746531408086144819390e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.758 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.32 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 1.342581311510171002862227001354 y[1] (numeric) = 1.3425813115101710028622270013534 absolute error = 6e-31 relative error = 4.4690030678671082909717847592648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.769 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.37 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop bytes used=104030928, alloc=4521156, time=3.54 x[1] = 1.37 y[1] (analytic) = 1.348713022522228302288614083143 y[1] (numeric) = 1.348713022522228302288614083143 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 = 3.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.42 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 1.354854839061078105833457796115 y[1] (numeric) = 1.3548548390610781058334577961146 absolute error = 4e-31 relative error = 2.9523458046413460169124072139303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.791 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.47 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 1.361006750712743567288848347412 y[1] (numeric) = 1.3610067507127435672888483474138 absolute error = 1.8e-30 relative error = 1.3225503834256227765203864348541e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.803 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.52 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.367168747116811910494757616179 y[1] (numeric) = 1.3671687471168119104947576161794 absolute error = 4e-31 relative error = 2.9257544165162495752751888062540e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.814 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.57 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 1.373340817966032659919284048473 y[1] (numeric) = 1.3733408179660326599192840484731 absolute error = 1e-31 relative error = 7.2815137139886085091409903243248e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.825 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.62 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop bytes used=108031800, alloc=4521156, time=3.67 x[1] = 1.42 y[1] (analytic) = 1.379522953005920037035561281787 y[1] (numeric) = 1.3795229530059200370355612817869 absolute error = 1e-31 relative error = 7.2488826504919243241055737484529e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.836 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.68 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 1.385715142034359467350710755054 y[1] (numeric) = 1.3857151420343594673507107550531 absolute error = 9e-31 relative error = 6.4948413472534896430979444901829e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.847 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.73 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 1.39191737490121814383011537979 y[1] (numeric) = 1.3919173749012181438301153797899 absolute error = 1e-31 relative error = 7.1843344873180291294248635379713e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.859 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.78 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 1.398129641507959593331359160529 y[1] (numeric) = 1.3981296415079595933313591605284 absolute error = 6e-31 relative error = 4.2914475323823837425160343782435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.83 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 1.404351931807262193516783208489 y[1] (numeric) = 1.4043519318072621935167832084892 absolute error = 2e-31 relative error = 1.4241444432138869846339248491512e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.881 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.88 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 1.410584235802641588552109613773 y[1] (numeric) = 1.4105842358026415885521096137729 absolute error = 1e-31 relative error = 7.0892611346318245086854960873952e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.892 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.93 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop bytes used=112032884, alloc=4521156, time=3.80 x[1] = 1.48 y[1] (analytic) = 1.416826543548076952721330069544 y[1] (numeric) = 1.4168265435480769527213300695434 absolute error = 6e-31 relative error = 4.2348162005594179791297665113329e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.904 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.98 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 1.423078845147641051895386377667 y[1] (numeric) = 1.4230788451476410518953863776671 absolute error = 1e-31 relative error = 7.0270175360259281623245589217365e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.915 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.03 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 1.42934113075513405358441710218 y[1] (numeric) = 1.4293411307551340535844171021802 absolute error = 2e-31 relative error = 1.3992460980559494723368326386358e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.926 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.08 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 1.435613390573721037080832686153 y[1] (numeric) = 1.4356133905737210370808326861518 absolute error = 1.2e-30 relative error = 8.3587963714969130212677173869390e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.937 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.13 Order of pole (six term test) = -2.491 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 1.441895614855573155963526457673 y[1] (numeric) = 1.4418956148555731559635264576727 absolute error = 3e-31 relative error = 2.0805944404654380537499975395724e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.948 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.18 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 1.448187793901512405982439620435 y[1] (numeric) = 1.4481877939015124059824396204356 absolute error = 6e-31 relative error = 4.1431090810644167362360326118091e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.23 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop bytes used=116033888, alloc=4521156, time=3.94 x[1] = 1.54 y[1] (analytic) = 1.454489918060659952077775608438 y[1] (numeric) = 1.4544899180606599520777756084387 absolute error = 7e-31 relative error = 4.8126837546824871384742531764317e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.971 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.28 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 1.460801977730087969009696893786 y[1] (numeric) = 1.4608019777300879690096968937854 absolute error = 6e-31 relative error = 4.1073328839020907737621314715755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.982 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.33 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 1.467123963354474950782622232888 y[1] (numeric) = 1.4671239633544749507826222328879 absolute error = 1e-31 relative error = 6.8160566181031552449438912884523e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.993 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.38 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 1.473455865425764444743554320063 y[1] (numeric) = 1.4734558654257644447435543200621 absolute error = 9e-31 relative error = 6.1080892961794907595471762631000e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.004 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.43 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 1.479797674482827166916480110816 y[1] (numeric) = 1.4797976744828271669164801108147 absolute error = 1.3e-30 relative error = 8.7849847476908324312367763175471e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.016 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.48 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop bytes used=120034580, alloc=4586680, time=4.08 x[1] = 1.59 y[1] (analytic) = 1.486149381111126455805065401725 y[1] (numeric) = 1.4861493811111264558050654017248 absolute error = 2e-31 relative error = 1.3457597368204606412186667218520e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.027 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.53 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 1.492510975942387022553872003069 y[1] (numeric) = 1.4925109759423870225538720030694 absolute error = 4e-31 relative error = 2.6800472924323777329550861424534e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.038 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.58 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 1.498882449654266956004414246585 y[1] (numeric) = 1.4988824496542669560044142465853 absolute error = 3e-31 relative error = 2.0014911781053822049465485881843e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.049 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.63 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 1.505263792970032941816789867771 y[1] (numeric) = 1.505263792970032941816789867772 absolute error = 1.0e-30 relative error = 6.6433538405046070028405008230237e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.061 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.68 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 1.511654996658238655450610882814 y[1] (numeric) = 1.511654996658238655450610882813 absolute error = 1.0e-30 relative error = 6.6152660640864750335715253303891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.072 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.73 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 1.518056051532406289410759649683 y[1] (numeric) = 1.5180560515324062894107596496829 absolute error = 1e-31 relative error = 6.5873720472346654421152413860068e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.083 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.78 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop bytes used=124035848, alloc=4586680, time=4.22 x[1] = 1.65 y[1] (analytic) = 1.524466948450711175764335027436 y[1] (numeric) = 1.5244669484507111757643350274357 absolute error = 3e-31 relative error = 1.9679009787971113402312794600636e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.094 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.83 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 1.530887678315669465525259198557 y[1] (numeric) = 1.5308876783156694655252591985557 absolute error = 1.3e-30 relative error = 8.4918052344003492464665610469637e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.105 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.88 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 1.537318232073828827082607813792 y[1] (numeric) = 1.5373182320738288270826078137907 absolute error = 1.3e-30 relative error = 8.4562842804922139569695584692115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.117 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.93 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 1.543758600715462126418020056193 y[1] (numeric) = 1.5437586007154621264180200561936 absolute error = 6e-31 relative error = 3.8866180225452813704261487354704e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.128 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.98 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 1.550208775274264052416751414589 y[1] (numeric) = 1.5502087752742640524167514145882 absolute error = 8e-31 relative error = 5.1605952227851595287972834903793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.139 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.02 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 1.556668746827050651126255962643 y[1] (numeric) = 1.5566687468270506511262559626426 absolute error = 4e-31 relative error = 2.5695897140307968602868703061303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.07 Order of pole (six term test) = -2.49 bytes used=128037024, alloc=4586680, time=4.36 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 1.563138506493461733355827582284 y[1] (numeric) = 1.5631385064934617333558275822845 absolute error = 5e-31 relative error = 3.1986928728512606102289217975583e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.161 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.12 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 1.569618045435666120540987062653 y[1] (numeric) = 1.5696180454356661205409870626526 absolute error = 4e-31 relative error = 2.5483906811798615110261212142538e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.173 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.17 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 1.576107354858069694317166068635 y[1] (numeric) = 1.5761073548580696943171660686348 absolute error = 2e-31 relative error = 1.2689490940038804227316900745905e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.184 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.22 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 1.582606426007026215758996948603 y[1] (numeric) = 1.5826064260070262157589969486016 absolute error = 1.4e-30 relative error = 8.8461665325866969058433659843691e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.195 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.27 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 1.589115250170550880744352314716 y[1] (numeric) = 1.5891152501705508807443523147168 absolute error = 8e-31 relative error = 5.0342478301315178988344143581818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.206 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.32 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop bytes used=132037836, alloc=4586680, time=4.50 x[1] = 1.76 y[1] (analytic) = 1.595633818678036578396369198231 y[1] (numeric) = 1.5956338186780365783963691982307 absolute error = 3e-31 relative error = 1.8801306194960595074443614361079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.218 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.37 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 1.602162122899972820042214220222 y[1] (numeric) = 1.6021621228999728200422142202216 absolute error = 4e-31 relative error = 2.4966262420184118173649434803029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.229 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.42 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 1.608700154247667306604469538238 y[1] (numeric) = 1.6087001542476673066044695382382 absolute error = 2e-31 relative error = 1.2432397639293631572587255974892e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.46 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 1.615247904172970102809911392653 y[1] (numeric) = 1.6152479041729701028099113926534 absolute error = 4e-31 relative error = 2.4764000557846610446692502695373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.251 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.51 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 1.621805364168000387061277189999 y[1] (numeric) = 1.6218053641680003870612771899994 absolute error = 4e-31 relative error = 2.4663872055029446769251920461858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.262 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.56 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 1.628372525764875746270532870161 y[1] (numeric) = 1.6283725257648757462705328701601 absolute error = 9e-31 relative error = 5.5269908191140345926677736362661e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.274 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.61 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop bytes used=136038868, alloc=4586680, time=4.63 x[1] = 1.82 y[1] (analytic) = 1.634949380535443985397315886864 y[1] (numeric) = 1.6349493805354439853973158868644 absolute error = 4e-31 relative error = 2.4465589256898000954129098686427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.285 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.66 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 1.641535920091017421873793082945 y[1] (numeric) = 1.6415359200910174218737930829441 absolute error = 9e-31 relative error = 5.4826701565573913834098499281853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.296 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.71 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 1.648132136082109635527286265967 y[1] (numeric) = 1.6481321360821096355272862659658 absolute error = 1.2e-30 relative error = 7.2809696123795272194378656657712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.307 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.75 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 1.65473802019817464503482727907 y[1] (numeric) = 1.6547380201981746450348272790708 absolute error = 8e-31 relative error = 4.8346021559605576923034051075032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.318 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.8 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 1.661353564167348482359451481218 y[1] (numeric) = 1.6613535641673484823594514812181 absolute error = 1e-31 relative error = 6.0191883387639321105234334338564e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.85 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop bytes used=140039544, alloc=4586680, time=4.77 x[1] = 1.87 y[1] (analytic) = 1.667978759756193137026663317276 y[1] (numeric) = 1.6679787597561931370266633172768 absolute error = 8e-31 relative error = 4.7962241444665352709763291750819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.341 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.9 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 1.674613598769442842501246517416 y[1] (numeric) = 1.6746135987694428425012465174154 absolute error = 6e-31 relative error = 3.5829160854832320922921006554008e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.352 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.95 Order of pole (six term test) = -2.49 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 1.681258073049752677319577867309 y[1] (numeric) = 1.6812580730497526773195778673095 absolute error = 5e-31 relative error = 2.9739634147481874175457437399256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.363 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.99 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 1.687912174477449454020967963869 y[1] (numeric) = 1.6879121744774494540209679638693 absolute error = 3e-31 relative error = 1.7773436588480984796045115996379e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.375 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.04 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 1.694575894970284869303422592577 y[1] (numeric) = 1.6945758949702848693034225925762 absolute error = 8e-31 relative error = 4.7209452369439513977786011834159e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.386 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.09 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 1.701249226483190889204719227647 y[1] (numeric) = 1.7012492264831908892047192276469 absolute error = 1e-31 relative error = 5.8780335322602449494204887172271e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.397 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.14 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop bytes used=144040388, alloc=4586680, time=4.91 x[1] = 1.93 y[1] (analytic) = 1.707932161008037343478946846628 y[1] (numeric) = 1.7079321610080373434789468466272 absolute error = 8e-31 relative error = 4.6840267913675951136405758786692e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.408 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.18 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 1.714624690573391703701783299878 y[1] (numeric) = 1.7146246905733917037017832998776 absolute error = 4e-31 relative error = 2.3328720401561175036950090577282e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.419 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.23 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 1.721326807244281019994899831641 y[1] (numeric) = 1.7213268072442810199948998316397 absolute error = 1.3e-30 relative error = 7.5523136834265970448522224461238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.431 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.28 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 1.728038503121955991611101439809 y[1] (numeric) = 1.7280385031219559916111014398086 absolute error = 4e-31 relative error = 2.3147632374934997348415891960770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.442 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.33 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 1.734759770343657146967246551583 y[1] (numeric) = 1.7347597703436571469672465515823 absolute error = 7e-31 relative error = 4.0351408417854277371794287661415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.453 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.37 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 1.741490601082383109051749544783 y[1] (numeric) = 1.7414906010823831090517495447824 absolute error = 6e-31 relative error = 3.4453243653860888492316060726828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.464 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.42 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop bytes used=148041192, alloc=4586680, time=5.04 x[1] = 1.99 y[1] (analytic) = 1.748230987546660922467662177832 y[1] (numeric) = 1.7482309875466609224676621778336 absolute error = 1.6e-30 relative error = 9.1521086824191498129214016126102e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.475 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.47 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 1.754980921980318418701059934097 y[1] (numeric) = 1.7549809219803184187010599340973 absolute error = 3e-31 relative error = 1.7094202919395861640311704920757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.487 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.52 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 1.761740396662258596527829332844 y[1] (numeric) = 1.7617403966622585965278293328441 absolute error = 1e-31 relative error = 5.6762051996682968214482075585499e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.498 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.56 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 1.768509403906235994790062922447 y[1] (numeric) = 1.7685094039062359947900629224476 absolute error = 6e-31 relative error = 3.3926876423429592245314033790274e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.509 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.61 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 1.775287936060635035086218334316 y[1] (numeric) = 1.7752879360606350350862183343161 absolute error = 1e-31 relative error = 5.6328890637256319270026407509186e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.66 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop bytes used=152042104, alloc=4586680, time=5.18 x[1] = 2.04 y[1] (analytic) = 1.782075985508250312227082741993 y[1] (numeric) = 1.7820759855082503122270827419927 absolute error = 3e-31 relative error = 1.6834299010793281225682553974062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.532 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.7 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 1.788873544666068810612498611489 y[1] (numeric) = 1.7888735446660688106124986114891 absolute error = 1e-31 relative error = 5.5901100610589621646489591556551e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.543 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.75 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 1.795680605985054024981843036127 y[1] (numeric) = 1.7956806059850540249818430361273 absolute error = 3e-31 relative error = 1.6706757259620199282052443125825e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.554 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.8 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 1.802497161949931964284501575421 y[1] (numeric) = 1.802497161949931964284501575421 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 = 4.565 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.84 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 1.809323205078979017705126825172 y[1] (numeric) = 1.8093232050789790177051268251727 absolute error = 7e-31 relative error = 3.8688499546958731626556436709356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.576 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.89 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 1.816158727923811662162408550352 y[1] (numeric) = 1.8161587279238116621624085503518 absolute error = 2e-31 relative error = 1.1012253330337217792499507512025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.588 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.94 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop bytes used=156042888, alloc=4586680, time=5.32 x[1] = 2.1 y[1] (analytic) = 1.82300372306917799087949092478 y[1] (numeric) = 1.8230037230691779908794909247795 absolute error = 5e-31 relative error = 2.7427261594299353577118365324086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.599 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.98 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 1.829858183132751042899136291371 y[1] (numeric) = 1.8298581831327510428991362913723 absolute error = 1.3e-30 relative error = 7.1043756941555763818739454253359e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.03 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 1.836722100764923913687335211545 y[1] (numeric) = 1.8367221007649239136873352115454 absolute error = 4e-31 relative error = 2.1777927092694938867593708117758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.621 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.08 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 1.843595468648606627235379058637 y[1] (numeric) = 1.8435954686486066272353790586368 absolute error = 2e-31 relative error = 1.0848366867955263033204366759708e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.632 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.12 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 1.850478279499024750332522031357 y[1] (numeric) = 1.8504782794990247503325220313573 absolute error = 3e-31 relative error = 1.6212024930182819134204436541275e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.644 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.17 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 1.857370526063519729939340617729 y[1] (numeric) = 1.8573705260635197299393406177279 absolute error = 1.1e-30 relative error = 5.9223508964111848248710444530401e-29 % Correct digits = 31 h = 0.01 bytes used=160044180, alloc=4586680, time=5.45 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.655 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.22 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 1.864272201121350934845825057915 y[1] (numeric) = 1.8642722011213509348458250579135 absolute error = 1.5e-30 relative error = 8.0460353327038673632906070720207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.666 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.26 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 1.871183297483499383048182533638 y[1] (numeric) = 1.8711832974834993830481825336392 absolute error = 1.2e-30 relative error = 6.4130542508253761022490605374706e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.677 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.31 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 1.878103807992473136524367452921 y[1] (numeric) = 1.8781038079924731365243674529208 absolute error = 2e-31 relative error = 1.0649038628689130403970130452473e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.689 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.35 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 1.885033725522114345330550638822 y[1] (numeric) = 1.8850337255221143453305506388223 absolute error = 3e-31 relative error = 1.5914834622754898743202244403268e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.4 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 1.891973042977407923179165376974 y[1] (numeric) = 1.8919730429774079231791653769729 absolute error = 1.1e-30 relative error = 5.8140363261673338520816839731012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.711 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.45 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop bytes used=164045588, alloc=4586680, time=5.59 x[1] = 2.21 y[1] (analytic) = 1.898921753294291836893891638115 y[1] (numeric) = 1.8989217532942918368938916381149 absolute error = 1e-31 relative error = 5.2661464237016490145060987892413e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.722 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.49 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 1.905879849439468992368026512432 y[1] (numeric) = 1.9058798494394689923680265124319 absolute error = 1e-31 relative error = 5.2469204724217329961127320565063e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.733 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.54 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 1.912847324410220699880203780022 y[1] (numeric) = 1.9128473244102206998802037800231 absolute error = 1.1e-30 relative error = 5.7505896365208230777662322691272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.745 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.58 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 1.919824171234221701845432099646 y[1] (numeric) = 1.9198241712342217018454320996459 absolute error = 1e-31 relative error = 5.2088103430696849877592927522495e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.756 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.63 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 1.926810382969356746299981752862 y[1] (numeric) = 1.9268103829693567462999817528629 absolute error = 9e-31 relative error = 4.6709318568910434140556577889963e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.767 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.68 Order of pole (six term test) = -2.489 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 1.933805952703538689635825212796 y[1] (numeric) = 1.9338059527035386896358252127961 absolute error = 1e-31 relative error = 5.1711496626740634535039169374474e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.778 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.72 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop bytes used=168046588, alloc=4586680, time=5.73 x[1] = 2.27 y[1] (analytic) = 1.940810873554528112314186776158 y[1] (numeric) = 1.9408108735545281123141867761573 absolute error = 7e-31 relative error = 3.6067398917544921113068739196863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.789 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.77 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 1.947825138669754431498339672178 y[1] (numeric) = 1.9478251386697544314983396721773 absolute error = 7e-31 relative error = 3.5937517495952292407490654793907e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.801 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.81 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 1.954848741226138494753162844818 y[1] (numeric) = 1.9548487412261384947531628448177 absolute error = 3e-31 relative error = 1.5346455900819783970586407791717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.812 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.86 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 1.961881674429916639163190257663 y[1] (numeric) = 1.9618816744299166391631902576634 absolute error = 4e-31 relative error = 2.0388589445193322167932332224523e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.823 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.9 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 1.96892393151646620042200824194 y[1] (numeric) = 1.9689239315164662004220082419405 absolute error = 5e-31 relative error = 2.5394581882851093643220250770094e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.834 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.95 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop bytes used=172047580, alloc=4586680, time=5.87 x[1] = 2.32 y[1] (analytic) = 1.975975505750132456643935154922 y[1] (numeric) = 1.9759755057501324566439351549224 absolute error = 4e-31 relative error = 2.0243165911520216048700753233472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.846 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 1.983036390424056991844005430289 y[1] (numeric) = 1.9830363904240569918440054302885 absolute error = 5e-31 relative error = 2.5213859030245978888393005366215e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.857 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.04 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 1.990106578860007464224428932907 y[1] (numeric) = 1.9901065788600074642244289329078 absolute error = 8e-31 relative error = 4.0198852086518095591331027971973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.868 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.09 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 1.997186064408208764594957307424 y[1] (numeric) = 1.9971860644082087645949573074236 absolute error = 4e-31 relative error = 2.0028179002867467330851957743738e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.879 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.13 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 2.004274840447175550441011664893 y[1] (numeric) = 2.004274840447175550441011664893 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 = 4.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.18 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 2.01137290038354614133705944092 y[1] (numeric) = 2.0113729003835461413370594409189 absolute error = 1.1e-30 relative error = 5.4689013647854278956346538233335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.902 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.22 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop bytes used=176048528, alloc=4586680, time=6.01 x[1] = 2.38 y[1] (analytic) = 2.018480237651917761583620584151 y[1] (numeric) = 2.0184802376519177615836205841509 absolute error = 1e-31 relative error = 4.9542223963673390303165815127306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.913 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.27 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 2.02559684571468311612448146401 y[1] (numeric) = 2.0255968457146831161244814640098 absolute error = 2e-31 relative error = 9.8736330688466693138470678991656e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.924 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.31 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 2.032722718061868285976245175895 y[1] (numeric) = 2.032722718061868285976245175895 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 = 4.935 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.36 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 2.039857848210971929575294532196 y[1] (numeric) = 2.0398578482109719295752945321966 absolute error = 6e-31 relative error = 2.9413814326631701071035155484694e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.946 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.4 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 2.047002229706805776617633345025 y[1] (numeric) = 2.0470022297068057766176333450249 absolute error = 1e-31 relative error = 4.8851925292882119770323829984289e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.958 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.45 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 2.054155856121336401134946163024 y[1] (numeric) = 2.0541558561213364011349461630236 absolute error = 4e-31 relative error = 1.9472719112720164668240662051849e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.969 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.49 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop bytes used=180049500, alloc=4586680, time=6.14 x[1] = 2.44 y[1] (analytic) = 2.061318721053528260715619114141 y[1] (numeric) = 2.0613187210535282607156191141401 absolute error = 9e-31 relative error = 4.3661370306675094126321236998573e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.54 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 2.068490818129187988942436803759 y[1] (numeric) = 2.0684908181291879889424368037601 absolute error = 1.1e-30 relative error = 5.3178867914670109500030804857519e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.991 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.58 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 2.075672141000809928279253396478 y[1] (numeric) = 2.075672141000809928279253396478 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 = 5.003 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.63 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 2.082862683347422890797170358689 y[1] (numeric) = 2.0828626833474228907971703586884 absolute error = 6e-31 relative error = 2.8806507735580742462576198798390e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.014 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.67 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 2.090062438874438134286678379004 y[1] (numeric) = 2.0900624388744381342866783790039 absolute error = 1e-31 relative error = 4.7845460566169987658728247709454e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.025 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.71 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop bytes used=184050320, alloc=4586680, time=6.28 x[1] = 2.49 y[1] (analytic) = 2.097271401313498541455875483534 y[1] (numeric) = 2.0972714013134985414558754835337 absolute error = 3e-31 relative error = 1.4304300330997372289865848832163e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.036 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.76 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 2.104489564422328990066295356978 y[1] (numeric) = 2.1044895644223289900662953569773 absolute error = 7e-31 relative error = 3.3262222433122219651196625994799e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.047 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.8 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 2.111716921984587902007106681917 y[1] (numeric) = 2.1117169219845879020071066819169 absolute error = 1e-31 relative error = 4.7354831965839518574779179415286e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.059 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.85 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 2.118953467809719959455512526386 y[1] (numeric) = 2.1189534678097199594555125263865 absolute error = 5e-31 relative error = 2.3596554034611746961880954664116e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.89 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 2.12619919573280997641612436249 y[1] (numeric) = 2.1261991957328099764161243624894 absolute error = 6e-31 relative error = 2.8219369154318847701165505295260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.081 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.94 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 2.133454099614437914074943429741 y[1] (numeric) = 2.1334540996144379140749434297407 absolute error = 3e-31 relative error = 1.4061703978267758334956249232658e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.092 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.98 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop bytes used=188051572, alloc=4586680, time=6.42 x[1] = 2.55 y[1] (analytic) = 2.140718173340535028544387447776 y[1] (numeric) = 2.1407181733405350285443874477762 absolute error = 2e-31 relative error = 9.3426590426849696932146305176685e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.103 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.03 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 2.147991410822241139714587068425 y[1] (numeric) = 2.1479914108222411397145870684241 absolute error = 9e-31 relative error = 4.1899608884166076733746271043324e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.115 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.07 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 2.155273805995763010062977237196 y[1] (numeric) = 2.1552738059957630100629772371954 absolute error = 6e-31 relative error = 2.7838690301476225638621828056925e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.126 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.11 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 2.162565352822233822409056488532 y[1] (numeric) = 2.1625653528222338224090564885326 absolute error = 6e-31 relative error = 2.7744826264647962161720290698762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.16 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 2.169866045287573745734114199274 y[1] (numeric) = 2.1698660452875737457341141992731 absolute error = 9e-31 relative error = 4.1477214778054302418311987607187e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.148 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.2 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 2.177175877402351578316763447057 y[1] (numeric) = 2.1771758774023515783167634470576 absolute error = 6e-31 relative error = 2.7558637142162189614225669550461e-29 % Correct digits = 31 h = 0.01 bytes used=192052452, alloc=4586680, time=6.55 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.159 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.25 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 2.184494843201647457564296258183 y[1] (numeric) = 2.1844948432016474575642962581833 absolute error = 3e-31 relative error = 1.3733152125930994834334019426411e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.171 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.29 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 2.191822936744916626047229005072 y[1] (numeric) = 2.1918229367449166260472290050707 absolute error = 1.3e-30 relative error = 5.9311360338743157294067121510243e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.182 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.33 Order of pole (six term test) = -2.488 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 2.199160152115854243369958290307 y[1] (numeric) = 2.1991601521158542433699582903074 absolute error = 4e-31 relative error = 1.8188761724113285394149137567751e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.193 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.38 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 2.206506483422261233634231047695 y[1] (numeric) = 2.2065064834222612336342310476953 absolute error = 3e-31 relative error = 1.3596153115974720484231008758895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.204 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.42 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 2.21386192479591115837417547996 y[1] (numeric) = 2.2138619247959111583741754799605 absolute error = 5e-31 relative error = 2.2584967671192655743501440249643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.216 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.47 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=196053496, alloc=4586680, time=6.69 x[1] = 2.66 y[1] (analytic) = 2.221226470392418104961969991418 y[1] (numeric) = 2.2212264703924181049619699914175 absolute error = 5e-31 relative error = 2.2510086506922742781119192533065e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.227 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.51 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 2.22860011439110558060187310082 y[1] (numeric) = 2.22860011439110558060187310082 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 = 5.238 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.55 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 2.235982850994876402147325569533 y[1] (numeric) = 2.2359828509948764021473255695342 absolute error = 1.2e-30 relative error = 5.3667674573893666943067637919935e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.249 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.6 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 2.243374674430083572091193293723 y[1] (numeric) = 2.2433746744300835720911932937237 absolute error = 7e-31 relative error = 3.1202991099907596678084825530282e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.64 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 2.250775578946402131192972043149 y[1] (numeric) = 2.2507755789464021311929720431485 absolute error = 5e-31 relative error = 2.2214564822764434894810872851503e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.272 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.68 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 2.258185558816701978318948566027 y[1] (numeric) = 2.2581855588167019783189485660273 absolute error = 3e-31 relative error = 1.3285002148238037958244046479646e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.283 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.73 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=200054620, alloc=4586680, time=6.83 x[1] = 2.72 y[1] (analytic) = 2.265604608336921648181932137169 y[1] (numeric) = 2.2656046083369216481819321371675 absolute error = 1.5e-30 relative error = 6.6207492449491549816765061803637e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.294 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.77 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 2.273032721825943037776261068025 y[1] (numeric) = 2.273032721825943037776261068025 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 = 5.305 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.81 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 2.280469893625467072411374339247 y[1] (numeric) = 2.2804698936254670724113743392455 absolute error = 1.5e-30 relative error = 6.5775917682268357546827766610655e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.316 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.86 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 2.28791611809989030235334323821 y[1] (numeric) = 2.2879161180998903023533432382106 absolute error = 6e-31 relative error = 2.6224737666444641492473517233539e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.328 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.9 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 2.295371389636182421188405137489 y[1] (numeric) = 2.2953713896361824211884051374903 absolute error = 1.3e-30 relative error = 5.6635715068577668701583531855466e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.339 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.94 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=204055424, alloc=4586680, time=6.96 x[1] = 2.77 y[1] (analytic) = 2.302835702643764697125754366439 y[1] (numeric) = 2.3028357026437646971257543664401 absolute error = 1.1e-30 relative error = 4.7767194104952766949275811841808e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.99 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 2.310309051554389308558646127649 y[1] (numeric) = 2.3103090515543893085586461276494 absolute error = 4e-31 relative error = 1.7313700941044129297618963609057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.361 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.03 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 2.317791430822019575303280809524 y[1] (numeric) = 2.3177914308220195753032808095253 absolute error = 1.3e-30 relative error = 5.6087876705064297960252734557503e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.373 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.07 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 2.325282834922711077033979667774 y[1] (numeric) = 2.3252828349227110770339796677743 absolute error = 3e-31 relative error = 1.2901656327324652152268893276573e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.384 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.12 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 2.332783258354493650530860126372 y[1] (numeric) = 2.3327832583544936505308601263723 absolute error = 3e-31 relative error = 1.2860174597258340646301764962119e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.395 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.16 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 2.340292695637254257452590937566 y[1] (numeric) = 2.3402926956372542574525909375661 absolute error = 1e-31 relative error = 4.2729697950354162029922313427339e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.406 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.2 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=208056624, alloc=4586680, time=7.10 x[1] = 2.83 y[1] (analytic) = 2.347811141312620714441874823105 y[1] (numeric) = 2.3478111413126207144418748231052 absolute error = 2e-31 relative error = 8.5185727455140812377090192883544e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.417 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.25 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 2.355338589943846277465089313014 y[1] (numeric) = 2.3553385899438462774650893130137 absolute error = 3e-31 relative error = 1.2737022238792101314282002482245e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.429 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.29 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 2.36287503611569507238003526384 y[1] (numeric) = 2.3628750361156950723800352638402 absolute error = 2e-31 relative error = 8.4642648021191105728348152231335e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.33 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 2.370420474434328363817016584895 y[1] (numeric) = 2.3704204744343283638170165848933 absolute error = 1.7e-30 relative error = 7.1717234066065179907235270912032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.451 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.38 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 2.377974899527191654548523294115 y[1] (numeric) = 2.377974899527191654548523294115 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 = 5.462 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.42 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 2.38553830604290260761163209354 y[1] (numeric) = 2.385538306042902607611632093539 absolute error = 1.0e-30 relative error = 4.1919259794188169471247165734491e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.473 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.46 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=212057564, alloc=4586680, time=7.24 x[1] = 2.89 y[1] (analytic) = 2.393110688651139783534892795808 y[1] (numeric) = 2.3931106886511397835348927958075 absolute error = 5e-31 relative error = 2.0893308544863903761383222621351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.485 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.5 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 2.400692042042532185107953422009 y[1] (numeric) = 2.4006920420425321851079534220088 absolute error = 2e-31 relative error = 8.3309311022599154749216579591286e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.496 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.55 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 2.408282360928549602217509583416 y[1] (numeric) = 2.4082823609285496022175095834153 absolute error = 7e-31 relative error = 2.9066359134487221750758749942629e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.507 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.59 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 2.415881640041393749357362500221 y[1] (numeric) = 2.4158816400413937493573625002209 absolute error = 1e-31 relative error = 4.1392756309984871038671456259113e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.518 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.63 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 2.42348987413389018850345203819 y[1] (numeric) = 2.4234898741338901885034520381906 absolute error = 6e-31 relative error = 2.4757685452035517284739351218092e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.67 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=216058448, alloc=4586680, time=7.38 x[1] = 2.94 y[1] (analytic) = 2.431107057979381030126713498676 y[1] (numeric) = 2.4311070579793810301267134986768 absolute error = 8e-31 relative error = 3.2906819030212574336662406248608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.541 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.72 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 2.438733186371618405197506324252 y[1] (numeric) = 2.4387331863716184051975063242529 absolute error = 9e-31 relative error = 3.6904406149449775618865273090858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.552 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.76 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 2.446368254124658701115195838556 y[1] (numeric) = 2.4463682541246587011151958385565 absolute error = 5e-31 relative error = 2.0438460119688982895330214383977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.563 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.8 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 2.454012256072757554575251799392 y[1] (numeric) = 2.4540122560727575545752517993923 absolute error = 3e-31 relative error = 1.2224877820296651275083925715879e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.574 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.84 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 2.461665187070265594463975805999 y[1] (numeric) = 2.4616651870702655944639758059998 absolute error = 8e-31 relative error = 3.2498326913097173251110612272987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.586 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.89 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 2.46932704199152492794769908992 y[1] (numeric) = 2.469327041991524927947699089919 absolute error = 1.0e-30 relative error = 4.0496863436667136225983121207269e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.597 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.93 Order of pole (six term test) = -2.487 TOP MAIN SOLVE Loop bytes used=220059532, alloc=4586680, time=7.51 x[1] = 3 y[1] (analytic) = 2.476997815730766362999018292563 y[1] (numeric) = 2.476997815730766362999018292563 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 = 5.608 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.97 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 2.484677503202007360677374588172 y[1] (numeric) = 2.4846775032020073606773745881716 absolute error = 4e-31 relative error = 1.6098668719965445922685754636396e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.619 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.01 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 2.49236609933895071055504578826 y[1] (numeric) = 2.4923660993389507105550457882599 absolute error = 1e-31 relative error = 4.0122516522160593115801765854207e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.06 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 2.500063599094883922752426451096 y[1] (numeric) = 2.5000635990948839227524264510956 absolute error = 4e-31 relative error = 1.5999592976147282345988421568690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.642 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.1 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 2.507769997442579330118331858112 y[1] (numeric) = 2.5077699974425793301183318581122 absolute error = 2e-31 relative error = 7.9752130460113864870300940990266e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.653 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.14 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop bytes used=224060556, alloc=4586680, time=7.65 x[1] = 3.05 y[1] (analytic) = 2.515485289374194894161992107025 y[1] (numeric) = 2.5154852893741948941619921070248 absolute error = 2e-31 relative error = 7.9507521210651250807413492549312e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.664 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.18 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 2.523209469901175708413416369405 y[1] (numeric) = 2.523209469901175708413416369406 absolute error = 1.0e-30 relative error = 3.9632064318431957486424207422707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.675 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.22 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 2.530942534054156192957918195836 y[1] (numeric) = 2.5309425340541561929579181958368 absolute error = 8e-31 relative error = 3.1608777727502598814132309431887e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.686 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.27 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 2.538684476882862973958814022689 y[1] (numeric) = 2.5386844768828629739588140226892 absolute error = 2e-31 relative error = 7.8780959911005186074033351799914e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.698 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.31 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 2.546435293456018442049651914602 y[1] (numeric) = 2.5464352934560184420496519146028 absolute error = 8e-31 relative error = 3.1416466856860168301645551104821e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.709 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.35 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 2.55419497886124498354380901874 y[1] (numeric) = 2.5541949788612449835438090187395 absolute error = 5e-31 relative error = 1.9575639453449970224259810529025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.39 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop bytes used=228061448, alloc=4586680, time=7.79 x[1] = 3.11 y[1] (analytic) = 2.561963528204969878474926947473 y[1] (numeric) = 2.5619635282049698784749269474731 absolute error = 1e-31 relative error = 3.9032561899920809696557150969581e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.731 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.43 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 2.569740936612330859546446869455 y[1] (numeric) = 2.5697409366123308595464468694564 absolute error = 1.4e-30 relative error = 5.4480199931967030137778974999350e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.743 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.47 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 2.577527199227082326132472790722 y[1] (numeric) = 2.5775271992270823261324727907225 absolute error = 5e-31 relative error = 1.9398437391851149080240337158957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.754 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.52 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 2.585322311211502207535344458783 y[1] (numeric) = 2.5853223112115022075353444587839 absolute error = 9e-31 relative error = 3.4811907053022451872450701125722e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.765 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.56 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 2.593126267746299469767652433965 y[1] (numeric) = 2.5931262677462994697676524339657 absolute error = 7e-31 relative error = 2.6994443298296226498332935770660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.776 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.6 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 2.600939064030522260187988856771 y[1] (numeric) = 2.600939064030522260187988856771 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 = 5.787 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.64 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop bytes used=232063016, alloc=4586680, time=7.93 x[1] = 3.17 y[1] (analytic) = 2.608760695281466684380509817805 y[1] (numeric) = 2.6087606952814666843805098178052 absolute error = 2e-31 relative error = 7.6664755169665504928021272919803e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.799 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.68 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 2.616591156734586209728400337705 y[1] (numeric) = 2.6165911567345862097284003377038 absolute error = 1.2e-30 relative error = 4.5861196041706332904119862559199e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.72 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 2.624430443643401690190591932248 y[1] (numeric) = 2.6244304436434016901905919322491 absolute error = 1.1e-30 relative error = 4.1913856115497191758830633564289e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.821 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.77 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 2.632278551279412006849596533106 y[1] (numeric) = 2.632278551279412006849596533106 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 = 5.832 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.81 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 2.640135474932005318856099938422 y[1] (numeric) = 2.6401354749320053188560999384225 absolute error = 5e-31 relative error = 1.8938422090361750080799448549639e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.843 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.85 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop bytes used=236063896, alloc=4586680, time=8.06 x[1] = 3.22 y[1] (analytic) = 2.648001209908370919453013584658 y[1] (numeric) = 2.6480012099083709194530135846593 absolute error = 1.3e-30 relative error = 4.9093633157553732563036741959148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.855 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.89 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 2.655875751533411691818025693067 y[1] (numeric) = 2.6558757515334116918180256930677 absolute error = 7e-31 relative error = 2.6356654658857590604115321723661e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.866 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.93 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 2.663759095149657159519332012881 y[1] (numeric) = 2.6637590951496571595193320128814 absolute error = 4e-31 relative error = 1.5016372941845438271226421211021e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.877 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.97 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 2.671651236117177126434172553316 y[1] (numeric) = 2.6716512361171771264341725533159 absolute error = 1e-31 relative error = 3.7430035271121015447017843697075e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.888 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.01 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 2.679552169813495901034063798817 y[1] (numeric) = 2.6795521698134959010340637988174 absolute error = 4e-31 relative error = 1.4927867593182225108514774526005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.06 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 2.687461891633507099994205706728 y[1] (numeric) = 2.6874618916335070999942057067285 absolute error = 5e-31 relative error = 1.8604914977830156054390002838227e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.911 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.1 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop bytes used=240065016, alloc=4586680, time=8.20 x[1] = 3.28 y[1] (analytic) = 2.695380396989389026137468905716 y[1] (numeric) = 2.6953803969893890261374689057168 absolute error = 8e-31 relative error = 2.9680411747950743174187545360007e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.922 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.14 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 2.703307681310520615775639403898 y[1] (numeric) = 2.7033076813105206157756394038971 absolute error = 9e-31 relative error = 3.3292547726705466930962918612647e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.933 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.18 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 2.711243740043397950562225082178 y[1] (numeric) = 2.711243740043397950562225082179 absolute error = 1.0e-30 relative error = 3.6883441544949158362009746021303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.944 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.22 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 2.719188568651551329022119446004 y[1] (numeric) = 2.7191885686515513290221194460039 absolute error = 1e-31 relative error = 3.6775676815083888251858871365129e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.956 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.26 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 2.727142162615462892973782545389 y[1] (numeric) = 2.7271421626154628929737825453893 absolute error = 3e-31 relative error = 1.1000526635996317397836686140734e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.967 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.3 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop bytes used=244065824, alloc=4586680, time=8.33 x[1] = 3.33 y[1] (analytic) = 2.735104517432484804109345512882 y[1] (numeric) = 2.7351045174324848041093455128812 absolute error = 8e-31 relative error = 2.9249339281227220915971548767519e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.978 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.34 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 2.743075628616757966047182533715 y[1] (numeric) = 2.7430756286167579660471825337144 absolute error = 6e-31 relative error = 2.1873257657958198335190684784452e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.989 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.38 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 2.751055491699131287220030835104 y[1] (numeric) = 2.7510554916991312872200308351037 absolute error = 3e-31 relative error = 1.0904905441028066642513729547369e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.42 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 2.759044102227081480009683908334 y[1] (numeric) = 2.7590441022270814800096839083332 absolute error = 8e-31 relative error = 2.8995549558422987358459836362776e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.012 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.47 Order of pole (six term test) = -2.486 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 2.767041455764633391586643970085 y[1] (numeric) = 2.7670414557646333915866439700851 absolute error = 1e-31 relative error = 3.6139682617211237953620354875400e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.023 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.51 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 2.775047547892280861959904808274 y[1] (numeric) = 2.7750475478922808619599048082735 absolute error = 5e-31 relative error = 1.8017709295819551166408588168764e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.034 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.55 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop bytes used=248066704, alloc=4586680, time=8.47 x[1] = 3.39 y[1] (analytic) = 2.783062374206908104788253692967 y[1] (numeric) = 2.7830623742069081047882536929675 absolute error = 5e-31 relative error = 1.7965820839444371741251262378524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.045 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.59 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 2.791085930321711606550138887966 y[1] (numeric) = 2.7910859303217116065501388879664 absolute error = 4e-31 relative error = 1.4331339485269606783542660147045e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.056 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.63 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 2.799118211866122539714255271369 y[1] (numeric) = 2.7991182118661225397142552713692 absolute error = 2e-31 relative error = 7.1451073110150479133347160638034e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.068 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.67 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 2.807159214485729685597562339356 y[1] (numeric) = 2.8071592144857296855975623393552 absolute error = 8e-31 relative error = 2.8498561673017169520112096523142e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.079 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.71 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 2.815208933842202862641473980988 y[1] (numeric) = 2.8152089338422028626414739809881 absolute error = 1e-31 relative error = 3.5521342234275946681725489677477e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.75 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 2.823267365613216855880455309234 y[1] (numeric) = 2.8232673656132168558804553092352 absolute error = 1.2e-30 relative error = 4.2503944706609770436848454514020e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.101 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.79 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop bytes used=252067572, alloc=4586680, time=8.61 x[1] = 3.45 y[1] (analytic) = 2.831334505492375843420235834134 y[1] (numeric) = 2.8313345054923758434202358341343 absolute error = 3e-31 relative error = 1.0595710235510631844665781368337e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.113 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.83 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 2.839410349189138315785307573264 y[1] (numeric) = 2.8394103491891383157853075732632 absolute error = 8e-31 relative error = 2.8174863849054405804065589600536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.124 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.87 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 2.847494892428742484037328405049 y[1] (numeric) = 2.8474948924287424840373284050496 absolute error = 6e-31 relative error = 2.1071152808573993959361896830814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.135 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.91 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 2.855588130952132172607502064166 y[1] (numeric) = 2.8555881309521321726075020641661 absolute error = 1e-31 relative error = 3.5019055765110366371953716022803e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.146 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.95 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 2.863690060515883192826963528881 y[1] (numeric) = 2.8636900605158831928269635288799 absolute error = 1.1e-30 relative error = 3.8411978138508434140776654399469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.157 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.99 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop bytes used=256068324, alloc=4586680, time=8.75 x[1] = 3.5 y[1] (analytic) = 2.871800676892130193179668924671 y[1] (numeric) = 2.8718006768921301931796689246722 absolute error = 1.2e-30 relative error = 4.1785629819498579293807714848180e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.169 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.03 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 2.879919975868493982342279128747 y[1] (numeric) = 2.8799199758684939823422791287479 absolute error = 9e-31 relative error = 3.1250868341527027639861047116737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.07 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 2.88804795324800932111504256524 y[1] (numeric) = 2.8880479532480093211150425652389 absolute error = 1.1e-30 relative error = 3.8088010234140948988324471155652e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.191 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.11 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 2.896184604849053179386731688709 y[1] (numeric) = 2.8961846048490531793867316887084 absolute error = 6e-31 relative error = 2.0716911449478253101972192226567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.202 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.15 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 2.904329926505273454315275722229 y[1] (numeric) = 2.9043299265052734543152757222292 absolute error = 2e-31 relative error = 6.8862699851960794681535001050776e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.213 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.19 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 2.912483914065518145943865606254 y[1] (numeric) = 2.9124839140655181459438656062541 absolute error = 1e-31 relative error = 3.4334953582768676366391876518795e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.225 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.23 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop bytes used=260069116, alloc=4586680, time=8.89 x[1] = 3.56 y[1] (analytic) = 2.920646563393764986509991990024 y[1] (numeric) = 2.9206465633937649865099919900239 absolute error = 1e-31 relative error = 3.4238993945162916657597376905234e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.236 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.28 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 2.92881787036905151974211952818 y[1] (numeric) = 2.9288178703690515197421195281799 absolute error = 1e-31 relative error = 3.4143468261274744663077916842015e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.247 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.32 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 2.936997830885405626475506708509 y[1] (numeric) = 2.9369978308854056264755067085081 absolute error = 9e-31 relative error = 3.0643536421294543631814224978343e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.258 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.36 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 2.945186440851776492955055818004 y[1] (numeric) = 2.9451864408517764929550558180046 absolute error = 6e-31 relative error = 2.0372224714795107463125326329679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.4 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 2.953383696191966018229028249649 y[1] (numeric) = 2.9533836961919660182290282496493 absolute error = 3e-31 relative error = 1.0157840323518207652246735209509e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.281 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.44 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop bytes used=264069948, alloc=4586680, time=9.03 x[1] = 3.61 y[1] (analytic) = 2.961589592844560657072991869135 y[1] (numeric) = 2.9615895928445606570729918691334 absolute error = 1.6e-30 relative error = 5.4025041277350820606343177271096e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.292 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.48 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 2.969804126762863694918485220335 y[1] (numeric) = 2.9698041267628636949184852203356 absolute error = 6e-31 relative error = 2.0203352624942644371151088160913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.303 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.52 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 2.978027293914827951295593486357 y[1] (numeric) = 2.9780272939148279512955934863577 absolute error = 7e-31 relative error = 2.3505493097069650632585742643294e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.314 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.55 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 2.986259090282988908332938791408 y[1] (numeric) = 2.9862590902829889083329387914079 absolute error = 1e-31 relative error = 3.3486712631663728731825023779554e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.326 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.59 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 2.994499511864398260892497997364 y[1] (numeric) = 2.9944995118643982608924979973648 absolute error = 8e-31 relative error = 2.6715649704745281174502419663206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.337 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.63 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 3.002748554670557884950179906074 y[1] (numeric) = 3.0027485546705578849501799060736 absolute error = 4e-31 relative error = 1.3321128716483069232285111389698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.348 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.67 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop bytes used=268071180, alloc=4586680, time=9.16 x[1] = 3.67 y[1] (analytic) = 3.011006214727354220866225933311 y[1] (numeric) = 3.0110062147273542208662259333108 absolute error = 2e-31 relative error = 6.6422978146562857436398642022223e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.359 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.71 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 3.019272488074993068222249003579 y[1] (numeric) = 3.0192724880749930682222490035782 absolute error = 8e-31 relative error = 2.6496449166469849931614245808509e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.75 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 3.02754737076793478893409968017 y[1] (numeric) = 3.0275473707679347889340996801694 absolute error = 6e-31 relative error = 1.9818021867905918697410272537782e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.382 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.79 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 3.035830858874829915381751370294 y[1] (numeric) = 3.0358308588748299153817513702936 absolute error = 4e-31 relative error = 1.3175964623676432760996790945117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.393 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.83 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 3.04412294847845516032903273403 y[1] (numeric) = 3.0441229484784551603290327340302 absolute error = 2e-31 relative error = 6.5700368672679944454410504846706e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.404 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.87 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 3.052423635675649825437310008912 y[1] (numeric) = 3.0524236356756498254373100089123 absolute error = 3e-31 relative error = 9.8282557012632818088791324598023e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.415 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.91 Order of pole (six term test) = -2.485 bytes used=272073232, alloc=4586680, time=9.30 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 3.060732916577252605208139597426 y[1] (numeric) = 3.0607329165772526052081395974265 absolute error = 5e-31 relative error = 1.6335956570792152878896671235356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.426 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.95 Order of pole (six term test) = -2.485 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 3.069050787308038783220476640311 y[1] (numeric) = 3.0690507873080387832204766403117 absolute error = 7e-31 relative error = 2.2808355042374260346668681544214e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.438 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.99 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 3.077377244006657817558243032293 y[1] (numeric) = 3.0773772440066578175582430322934 absolute error = 4e-31 relative error = 1.2998081427261460943346764408563e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.449 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.03 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 3.085712282825571312353932978405 y[1] (numeric) = 3.0857122828255713123539329784042 absolute error = 8e-31 relative error = 2.5925942754048475287018759323459e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.07 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 3.094055899930991372403470220589 y[1] (numeric) = 3.0940558999309913724034702205901 absolute error = 1.1e-30 relative error = 3.5552040285520826404060873935465e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.471 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.11 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop bytes used=276073956, alloc=4586680, time=9.44 x[1] = 3.78 y[1] (analytic) = 3.102408091502819337836732901975 y[1] (numeric) = 3.1024080915028193378367329019745 absolute error = 5e-31 relative error = 1.6116512891049027908135879713863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.483 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.15 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 3.110768853734584895857034030899 y[1] (numeric) = 3.1107688537345848958570340308985 absolute error = 5e-31 relative error = 1.6073196804697746020260636217064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.494 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.19 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 3.119138182833385566591391945603 y[1] (numeric) = 3.1191381828333855665913919456035 absolute error = 5e-31 relative error = 1.6030068906591574640850947012736e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.505 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.23 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 3.127516075019826560121650287086 y[1] (numeric) = 3.1275160750198265601216502870851 absolute error = 9e-31 relative error = 2.8776830507395379075656576882785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.516 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.27 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 3.135902526527961001794414924195 y[1] (numeric) = 3.1359025265279610017944149241956 absolute error = 6e-31 relative error = 1.9133247762784062805267110551576e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.527 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.31 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 3.144297533605230522935370142519 y[1] (numeric) = 3.1442975336052305229353701425185 absolute error = 5e-31 relative error = 1.5901803015018853639002900817325e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.539 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.35 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop bytes used=280074852, alloc=4586680, time=9.57 x[1] = 3.84 y[1] (analytic) = 3.152701092512406214120822247941 y[1] (numeric) = 3.152701092512406214120822247942 absolute error = 1.0e-30 relative error = 3.1718833173718161282993310787303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.38 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 3.161113199523529938186299529315 y[1] (numeric) = 3.1611131995235299381862995293159 absolute error = 9e-31 relative error = 2.8470982947894928598279969434938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.561 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.42 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 3.16953385092585600017871719615 y[1] (numeric) = 3.1695338509258560001787171961499 absolute error = 1e-31 relative error = 3.1550380814134195353461953034595e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.572 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.46 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 3.177963043019793171484998324015 y[1] (numeric) = 3.177963043019793171484998324015 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 = 6.583 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.5 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 3.186400772118847065396130812983 y[1] (numeric) = 3.1864007721188470653961308129839 absolute error = 9e-31 relative error = 2.8245034581809083408023904262031e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.595 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.54 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop bytes used=284075872, alloc=4586680, time=9.71 x[1] = 3.89 y[1] (analytic) = 3.194847034549562861391439648723 y[1] (numeric) = 3.1948470345495628613914396487225 absolute error = 5e-31 relative error = 1.5650201546206243330557579309603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.606 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.58 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 3.203301826651468375453367052982 y[1] (numeric) = 3.2033018266514683754533670529818 absolute error = 2e-31 relative error = 6.2435577670514896913899845803821e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.617 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.62 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 3.211765144777017473748284068053 y[1] (numeric) = 3.2117651447770174737482840680528 absolute error = 2e-31 relative error = 6.2271053761586716789690743159470e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.628 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.66 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 3.220236985291533827033809333432 y[1] (numeric) = 3.2202369852915338270338093334307 absolute error = 1.3e-30 relative error = 4.0369699681662052259051210029860e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.639 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.7 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 3.228717344573155003177787825924 y[1] (numeric) = 3.228717344573155003177787825925 absolute error = 1.0e-30 relative error = 3.0972051538695551326005557876480e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.651 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.74 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 3.237206219012776895198487639267 y[1] (numeric) = 3.2372062190127768951984876392662 absolute error = 8e-31 relative error = 2.4712667215991237054059971416219e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.662 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.77 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop bytes used=288076928, alloc=4586680, time=9.84 x[1] = 3.95 y[1] (analytic) = 3.245703605013998482259709918285 y[1] (numeric) = 3.2457036050139984822597099182851 absolute error = 1e-31 relative error = 3.0809960541535248198960840184640e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.673 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.81 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 3.254209498993066921078379229069 y[1] (numeric) = 3.2542094989930669210783792290706 absolute error = 1.6e-30 relative error = 4.9167086522704812278961413424352e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.684 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.85 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 3.262723897378822965225792284706 y[1] (numeric) = 3.2627238973788229652257922847066 absolute error = 6e-31 relative error = 1.8389542568466258104299433391879e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.696 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.89 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 3.27124679661264670982705535306 y[1] (numeric) = 3.2712467966126467098270553530598 absolute error = 2e-31 relative error = 6.1138768315218102165105799457610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.707 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.93 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 3.279778193148403659186338098467 y[1] (numeric) = 3.2797781931484036591863380984669 absolute error = 1e-31 relative error = 3.0489866726019539763966875672587e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.718 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.97 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop bytes used=292077944, alloc=4586680, time=9.98 x[1] = 4 y[1] (analytic) = 3.288318083452391114888417256633 y[1] (numeric) = 3.2883180834523911148884172566319 absolute error = 1.1e-30 relative error = 3.3451751688362054589817914468538e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.729 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.01 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 3.296866464003284881949580569668 y[1] (numeric) = 3.2968664640032848819495805696665 absolute error = 1.5e-30 relative error = 4.5497748130768861273605613121850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.05 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 3.305423331292086290613312929279 y[1] (numeric) = 3.3054233312920862906133129292783 absolute error = 7e-31 relative error = 2.1177317694020474568258525325368e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.752 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.08 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 3.313988681822069531408295759839 y[1] (numeric) = 3.3139886818220695314082957598386 absolute error = 4e-31 relative error = 1.2070047257375524484192804393033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.763 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.12 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 3.322562512108729301108120345272 y[1] (numeric) = 3.3225625121087293011081203452711 absolute error = 9e-31 relative error = 2.7087526471512416852912697218832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.774 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.16 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 3.331144818679728757253749047524 y[1] (numeric) = 3.3311448186797287572537490475226 absolute error = 1.4e-30 relative error = 4.2027593401204281166449590803821e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.785 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.2 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop bytes used=296078820, alloc=4586680, time=10.11 x[1] = 4.06 y[1] (analytic) = 3.339735598074847778921158120902 y[1] (numeric) = 3.3397355980748477789211581209021 absolute error = 1e-31 relative error = 2.9942490075455030414202079820314e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.796 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.24 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 3.348334846845931531437764995544 y[1] (numeric) = 3.3483348468459315314377649955441 absolute error = 1e-31 relative error = 2.9865591278661427708460308630350e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.808 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.28 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 3.356942561556839332772184343677 y[1] (numeric) = 3.356942561556839332772184343677 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 = 6.819 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.32 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 3.365558738783393819342573773193 y[1] (numeric) = 3.3655587387833938193425737731925 absolute error = 5e-31 relative error = 1.4856374195410523920404354930356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.35 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 3.374183375113330409009324393703 y[1] (numeric) = 3.3741833751133304090093243937031 absolute error = 1e-31 relative error = 2.9636800636729249862453509508383e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.841 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.39 Order of pole (six term test) = -2.484 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 3.38281646714624705903812651148 y[1] (numeric) = 3.3828164671462470590381265114806 absolute error = 6e-31 relative error = 1.7736699753804899467507461115332e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.853 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.43 Order of pole (six term test) = -2.483 bytes used=300079488, alloc=4586680, time=10.24 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 3.391458011493554316839499033804 y[1] (numeric) = 3.3914580114935543168394990338041 absolute error = 1e-31 relative error = 2.9485843451725734686899854679755e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.864 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.47 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 3.400108004778425661310715465084 y[1] (numeric) = 3.4001080047784256613107154650833 absolute error = 7e-31 relative error = 2.0587581306718425761668712505087e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.875 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.51 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 3.408766443635748132625692284387 y[1] (numeric) = 3.4087664436357481326256922843856 absolute error = 1.4e-30 relative error = 4.1070575621683758238831110707195e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.886 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.54 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 3.417433324712073248337829597921 y[1] (numeric) = 3.4174333247120732483378295979208 absolute error = 2e-31 relative error = 5.8523453421538361056309963970987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.897 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.58 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 3.426108644665568203680011815961 y[1] (numeric) = 3.426108644665568203680011815962 absolute error = 1.0e-30 relative error = 2.9187632492536229061938152634951e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.909 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.62 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop bytes used=304080364, alloc=4586680, time=10.38 x[1] = 4.17 y[1] (analytic) = 3.434792400165967353964990231568 y[1] (numeric) = 3.4347924001659673539649902315678 absolute error = 2e-31 relative error = 5.8227682112705299357317696799080e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.66 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 3.443484587894523977008182263485 y[1] (numeric) = 3.4434845878945239770081822634835 absolute error = 1.5e-30 relative error = 4.3560526022773821412646835522777e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.931 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.7 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 3.452185204543962313513536218614 y[1] (numeric) = 3.4521852045439623135135362186147 absolute error = 7e-31 relative error = 2.0277011762828373958337227823342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.942 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.74 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 3.46089424681842988338152814762 y[1] (numeric) = 3.4608942468184298833815281476202 absolute error = 2e-31 relative error = 5.7788532597856253018008822739369e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.953 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.77 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 3.469611711433450075916581094362 y[1] (numeric) = 3.4696117114334500759165810943622 absolute error = 2e-31 relative error = 5.7643337823923574727677991767849e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.965 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.81 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 3.47833759511587501192922912736 y[1] (numeric) = 3.4783375951158750119292291273613 absolute error = 1.3e-30 relative error = 3.7374175578167037279495232732607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.976 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.85 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop bytes used=308081264, alloc=4586680, time=10.51 x[1] = 4.23 y[1] (analytic) = 3.487071894603838675746191307992 y[1] (numeric) = 3.4870718946038386757461913079909 absolute error = 1.1e-30 relative error = 3.1545090931512596472329069031069e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.987 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.89 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 3.495814606646710315159176483141 y[1] (numeric) = 3.4958146066467103151591764831413 absolute error = 3e-31 relative error = 8.5816907861646860019672436013177e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.998 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.93 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 3.50456572800504810736071074548 y[1] (numeric) = 3.5045657280050481073607107454785 absolute error = 1.5e-30 relative error = 4.2801308818763844967299738568732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.009 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.96 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 3.513325255450553088932567807431 y[1] (numeric) = 3.5133252554505530889325678074304 absolute error = 6e-31 relative error = 1.7077838126975672589585142909335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.021 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 3.522093185766023347969490580584 y[1] (numeric) = 3.5220931857660233479694905805835 absolute error = 5e-31 relative error = 1.4196103669848091523081321643401e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.032 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.04 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop bytes used=312082080, alloc=4586680, time=10.65 x[1] = 4.28 y[1] (analytic) = 3.530869515745308476437822105337 y[1] (numeric) = 3.5308695157453084764378221053352 absolute error = 1.8e-30 relative error = 5.0978944194148437901775724769231e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.043 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.08 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 3.539654242193264280885417772124 y[1] (numeric) = 3.5396542421932642808854177721245 absolute error = 5e-31 relative error = 1.4125673463806641449923622526770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.054 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.11 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 3.548447361925707749635790622101 y[1] (numeric) = 3.5484473619257077496357906221005 absolute error = 5e-31 relative error = 1.4090669777574349591525644856758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.066 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.15 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 3.557248871769372274615849489934 y[1] (numeric) = 3.5572488717693722746158494899334 absolute error = 6e-31 relative error = 1.6866967188088826605078203037355e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.077 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.19 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 3.566058768561863125982827904798 y[1] (numeric) = 3.5660587685618631259828279047982 absolute error = 2e-31 relative error = 5.6084325295810235977204252143825e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.088 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.23 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 3.574877049151613177732072019883 y[1] (numeric) = 3.5748770491516131777320720198825 absolute error = 5e-31 relative error = 1.3986495007392200538473822163666e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.099 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.27 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop bytes used=316083876, alloc=4586680, time=10.79 x[1] = 4.34 y[1] (analytic) = 3.583703710397838882483260391378 y[1] (numeric) = 3.5837037103978388824832603913767 absolute error = 1.3e-30 relative error = 3.6275320312562409660012840429273e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.3 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 3.592538749170496493658369143249 y[1] (numeric) = 3.5925387491704964936583691432494 absolute error = 4e-31 relative error = 1.1134187490458063274501934612051e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.122 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.34 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 3.601382162350238533280274876225 y[1] (numeric) = 3.6013821623502385332802748762259 absolute error = 9e-31 relative error = 2.4990405334063904626436559873639e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.133 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.38 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 3.610233946828370503636306524283 y[1] (numeric) = 3.6102339468283705036363065242817 absolute error = 1.3e-30 relative error = 3.6008746777811006792952155837385e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.144 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.42 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 3.619094099506807841066318119993 y[1] (numeric) = 3.6190940995068078410663181199925 absolute error = 5e-31 relative error = 1.3815612035844481503519983026743e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.155 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.45 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 3.627962617298033110149958966361 y[1] (numeric) = 3.6279626172980331101499589663609 bytes used=320085244, alloc=4586680, time=10.92 absolute error = 1e-31 relative error = 2.7563679824925029202581752262378e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.166 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.49 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 3.63683949712505343658276786749 y[1] (numeric) = 3.6368394971250534365827678674898 absolute error = 2e-31 relative error = 5.4992803547723613201024398504016e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.178 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.53 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 3.645724735921358177045515659411 y[1] (numeric) = 3.6457247359213581770455156594108 absolute error = 2e-31 relative error = 5.4858776920099925564443395784270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.189 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.57 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 3.654618330630876824385867097072 y[1] (numeric) = 3.6546183306308768243858670970718 absolute error = 2e-31 relative error = 5.4725276870560404351242749138247e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.6 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 3.663520278207937146445930961722 y[1] (numeric) = 3.6635202782079371464459309617215 absolute error = 5e-31 relative error = 1.3648075130747797706835192473404e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.211 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.64 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 3.672430575617223556883617799047 y[1] (numeric) = 3.6724305756172235568836177990474 absolute error = 4e-31 relative error = 1.0891969004281917609759307133411e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.222 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.68 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop bytes used=324086168, alloc=4586680, time=11.06 x[1] = 4.45 y[1] (analytic) = 3.681349219833735716349929703679 y[1] (numeric) = 3.6813492198337357163499297036794 absolute error = 4e-31 relative error = 1.0865581505958448062020487527696e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.234 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.72 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 3.690276207842747362398367728575 y[1] (numeric) = 3.6902762078427473623983677285756 absolute error = 6e-31 relative error = 1.6258945569571512701099281424390e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.245 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.75 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 3.699211536639765366516561494448 y[1] (numeric) = 3.6992115366397653665165614944486 absolute error = 6e-31 relative error = 1.6219672599340427450133346944773e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.256 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.79 Order of pole (six term test) = -2.483 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 3.708155203230489016684004058785 y[1] (numeric) = 3.7081552032304890166840040587859 absolute error = 9e-31 relative error = 2.4270828772645048466189350508475e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.267 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.83 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 3.717107204630769523873414708413 y[1] (numeric) = 3.717107204630769523873414708414 absolute error = 1.0e-30 relative error = 2.6902640815798928478168534639940e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.279 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.86 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 3.726067537866569750926754674766 y[1] (numeric) = 3.726067537866569750926754674765 absolute error = 1.0e-30 relative error = 2.6837946168108613022629833552510e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.9 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop bytes used=328087096, alloc=4586680, time=11.20 x[1] = 4.51 y[1] (analytic) = 3.735036199973924162250287426718 y[1] (numeric) = 3.7350361999739241622502874267188 absolute error = 8e-31 relative error = 2.1418801777760149473236732988072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.301 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.94 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 3.744013187998898992786307740975 y[1] (numeric) = 3.7440131879988989927863077409742 absolute error = 8e-31 relative error = 2.1367446102068464645669019988826e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.312 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.98 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 3.752998498997552634732263732716 y[1] (numeric) = 3.7529984989975526347322637327158 absolute error = 2e-31 relative error = 5.3290722086198847121448408832341e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.323 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.01 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 3.761992130035896240490964978028 y[1] (numeric) = 3.7619921300358962404909649780276 absolute error = 4e-31 relative error = 1.0632664454728225951837209344737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.335 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.05 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 3.770994078189854540348409282288 y[1] (numeric) = 3.7709940781898545403484092822884 absolute error = 4e-31 relative error = 1.0607282634397751295302021161413e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.346 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.09 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop bytes used=332087928, alloc=4586680, time=11.34 x[1] = 4.56 y[1] (analytic) = 3.780004340545226873388472034262 y[1] (numeric) = 3.7800043405452268733884720342617 absolute error = 3e-31 relative error = 7.9364988230867500964396044038572e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.357 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.12 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 3.789022914197648430166286903018 y[1] (numeric) = 3.7890229141976484301662869030178 absolute error = 2e-31 relative error = 5.2784056610106664050964353290625e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.368 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.16 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 3.798049796252551705674606334383 y[1] (numeric) = 3.7980497962525517056746063343828 absolute error = 2e-31 relative error = 5.2658603949146584531562963477735e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.379 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.2 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 3.807084983825128161149766316701 y[1] (numeric) = 3.8070849838251281611497663167002 absolute error = 8e-31 relative error = 2.1013452638932386150159657680978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.391 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.23 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 3.816128474040290093276093625197 y[1] (numeric) = 3.8161284740402900932760936251963 absolute error = 7e-31 relative error = 1.8343197949488361707508190298104e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.402 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.27 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 3.825180264032632709359686614794 y[1] (numeric) = 3.825180264032632709359686614795 absolute error = 1.0e-30 relative error = 2.6142558807039504655493894447667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.413 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.31 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop bytes used=336089012, alloc=4586680, time=11.48 x[1] = 4.62 y[1] (analytic) = 3.834240350946396407054473989475 y[1] (numeric) = 3.8342403509463964070544739894753 absolute error = 3e-31 relative error = 7.8242356383827559229266864227666e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.424 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.35 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 3.843308731935429257235311191128 y[1] (numeric) = 3.8433087319354292572353111911271 absolute error = 9e-31 relative error = 2.3417322488864283595800967771449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.435 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.38 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 3.852385404163149688624612463782 y[1] (numeric) = 3.8523854041631496886246124637821 absolute error = 1e-31 relative error = 2.5957942809131505502234712732708e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.447 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.42 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 3.861470364802509372790639584294 y[1] (numeric) = 3.861470364802509372790639584295 absolute error = 1.0e-30 relative error = 2.5896871023925206092129338570048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.458 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.46 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 3.870563611035956308147077015283 y[1] (numeric) = 3.8705636110359563081470770152826 absolute error = 4e-31 relative error = 1.0334412250957425923205075827920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.469 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.49 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop bytes used=340090008, alloc=4586680, time=11.62 x[1] = 4.67 y[1] (analytic) = 3.879665140055398101594919120896 y[1] (numeric) = 3.8796651400553981015949191208951 absolute error = 9e-31 relative error = 2.3197878360892476812516015935923e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.53 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 3.888774949062165446458979364826 y[1] (numeric) = 3.8887749490621654464589793648246 absolute error = 1.4e-30 relative error = 3.6001054788157137543857397124672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.492 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.57 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 3.897893035266975795382505340606 y[1] (numeric) = 3.8978930352669757953825053406047 absolute error = 1.3e-30 relative error = 3.3351351313080862019116148724559e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.503 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.6 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 3.907019395889897226854448308456 y[1] (numeric) = 3.9070193958898972268544483084558 absolute error = 2e-31 relative error = 5.1189917360122609398594630876653e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.514 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.64 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 3.916154028160312504054892856613 y[1] (numeric) = 3.9161540281603125040548928566122 absolute error = 8e-31 relative error = 2.0428205689749520544784824449933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.525 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.68 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 3.925296929316883324715002578594 y[1] (numeric) = 3.9252969293168833247150025785922 absolute error = 1.8e-30 relative error = 4.5856403538706376010613874794220e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.536 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.71 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop bytes used=344091028, alloc=4586680, time=11.75 x[1] = 4.73 y[1] (analytic) = 3.934448096607514760698582456235 y[1] (numeric) = 3.9344480966075147606985824562336 absolute error = 1.4e-30 relative error = 3.5583135566260300187108671261495e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.548 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.75 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 3.943607527289319886022999141385 y[1] (numeric) = 3.9436075272893198860229991413843 absolute error = 7e-31 relative error = 1.7750245052431786050942419565319e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.559 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.79 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 3.952775218628584592047737701848 y[1] (numeric) = 3.9527752186285845920477377018477 absolute error = 3e-31 relative error = 7.5896043515493654475946492544991e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.82 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 3.961951167900732588569308789761 y[1] (numeric) = 3.9619511679007325885693087897608 absolute error = 2e-31 relative error = 5.0480177953826571896313945248294e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.581 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.86 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 3.971135372390290589571554738754 y[1] (numeric) = 3.9711353723902905895715547387531 absolute error = 9e-31 relative error = 2.2663543687211938282051938331324e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.592 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.89 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 3.980327829390853682390637921408 y[1] (numeric) = 3.980327829390853682390637921408 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 = 7.604 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.93 Order of pole (six term test) = -2.482 bytes used=348092480, alloc=4586680, time=11.89 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 3.989528536205050879064130908051 y[1] (numeric) = 3.9895285362050508790641309080507 absolute error = 3e-31 relative error = 7.5196855286907720647160031261720e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.615 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 48.97 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 3.998737490144510848643666655124 y[1] (numeric) = 3.9987374901445108486436666551237 absolute error = 3e-31 relative error = 7.5023679533701589498993167931611e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.626 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 4.007954688529827829260549196094 y[1] (numeric) = 4.0079546885298278292605491960938 absolute error = 2e-31 relative error = 4.9900763741758446413918290739097e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.637 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.04 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 4.017180128690527718743572176147 y[1] (numeric) = 4.0171801286905277187435721761463 absolute error = 7e-31 relative error = 1.7425158384126967664882209299009e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.648 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.08 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 4.026413807965034342598045116728 y[1] (numeric) = 4.0264138079650343425980451167268 absolute error = 1.2e-30 relative error = 2.9803196025857183415888838414696e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.11 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop bytes used=352094500, alloc=4586680, time=12.02 x[1] = 4.84 y[1] (analytic) = 4.035655723700635898164686557003 y[1] (numeric) = 4.0356557237006358981646865570037 absolute error = 7e-31 relative error = 1.7345384441220632088346650717791e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.671 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.15 Order of pole (six term test) = -2.482 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 4.044905873253451573786610223305 y[1] (numeric) = 4.0449058732534515737866102233039 absolute error = 1.1e-30 relative error = 2.7194699567019432740230016509780e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.682 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.19 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 4.054164253988398341822106138502 y[1] (numeric) = 4.0541642539883983418221061385013 absolute error = 7e-31 relative error = 1.7266197325659789737617367394542e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.693 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.22 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 4.063430863279157924350304102586 y[1] (numeric) = 4.0634308632791579243503041025855 absolute error = 5e-31 relative error = 1.2304872823565251648574452105635e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.704 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.26 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 4.072705698508143930426103242163 y[1] (numeric) = 4.0727056985081439304261032421626 absolute error = 4e-31 relative error = 9.8214805981812620152246655023336e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.716 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.29 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 4.081988757066469163749959317129 y[1] (numeric) = 4.0819887570664691637499593171304 absolute error = 1.4e-30 relative error = 3.4297007741052998342769890670835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.727 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.33 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop bytes used=356095432, alloc=4586680, time=12.16 x[1] = 4.9 y[1] (analytic) = 4.09128003635391309962724215184 y[1] (numeric) = 4.0912800363539130996272421518406 absolute error = 6e-31 relative error = 1.4665336879132598482444352576610e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.738 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.37 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 4.1005795337788895301009098784 y[1] (numeric) = 4.1005795337788895301009098783996 absolute error = 4e-31 relative error = 9.7547187343877696978950823195617e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.749 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.4 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 4.1098872467584143761501955823 y[1] (numeric) = 4.1098872467584143761501955823011 absolute error = 1.1e-30 relative error = 2.6764724527846876153541360052412e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.761 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.44 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 4.119203172718073665856866354678 y[1] (numeric) = 4.1192031727180736658568663546768 absolute error = 1.2e-30 relative error = 2.9131847827942289037692819792005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.772 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.47 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 4.128527309091991677449395598999 y[1] (numeric) = 4.1285273090919916774493955989975 absolute error = 1.5e-30 relative error = 3.6332568194393335453107741288082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.783 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.51 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop bytes used=360096532, alloc=4586680, time=12.30 x[1] = 4.95 y[1] (analytic) = 4.137859653322799246144087619697 y[1] (numeric) = 4.1378596533227992461440876196984 absolute error = 1.4e-30 relative error = 3.3833916983524727851279922292732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.794 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.55 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 4.147200202861602233710809931439 y[1] (numeric) = 4.1472002028616022337108099314391 absolute error = 1e-31 relative error = 2.4112653141509584685485449712986e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.805 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.58 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 4.156548955167950159699524255096 y[1] (numeric) = 4.1565489551679501596995242550944 absolute error = 1.6e-30 relative error = 3.8493471802146743935905434470259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.817 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.62 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 4.165905907709804993272262683815 y[1] (numeric) = 4.1659059077098049932722626838151 absolute error = 1e-31 relative error = 2.4004382771807421249121461515080e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.828 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.65 Order of pole (six term test) = -2.481 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 4.175271057963510104593571872656 y[1] (numeric) = 4.1752710579635101045935718726563 absolute error = 3e-31 relative error = 7.1851622525873829911895337173712e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.839 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 49.69 Order of pole (six term test) = -2.481 Finished! diff ( y , x , 1 ) = sinh(sqrt(0.1 * x + 0.2)); Iterations = 490 Total Elapsed Time = 12 Seconds Elapsed Time(since restart) = 11 Seconds Time to Timeout = 2 Minutes 47 Seconds Percent Done = 100.2 % > quit bytes used=363230824, alloc=4586680, time=12.40