|\^/| 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > 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 mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D2[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_0D3[1]; > #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := expt(array_tmp2[1] , array_tmp4[1] ) ; > array_tmp5_a1[1] := ln(array_tmp2[1] ) ; > array_tmp5_a1[2] := array_tmp2[2] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D2[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp5_a2[1] := (array_tmp5_a1[1] * array_tmp4[2] + array_tmp5_a1[2] * array_tmp4[1]) / glob_h; > array_tmp5[2] := array_tmp5[1] * array_tmp5_a2[1] * glob_h; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp5_a1[3] := -array_tmp5_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2; > array_tmp5_a2[2] := (array_tmp5_a1[2] * array_tmp4[2] + array_tmp5_a1[3] * array_tmp4[1]) * 2 / glob_h; > array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h/2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 4 > array_tmp5_a1[4] := -array_tmp5_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3; > array_tmp5_a2[3] := (array_tmp5_a1[3] * array_tmp4[2] + array_tmp5_a1[4] * array_tmp4[1]) * 3 / glob_h; > array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h/3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 5 > array_tmp5_a1[5] := -array_tmp5_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4; > array_tmp5_a2[4] := (array_tmp5_a1[4] * array_tmp4[2] + array_tmp5_a1[5] * array_tmp4[1]) * 4 / glob_h; > array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h/4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_tmp5[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_tmp6[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 expt LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp5_a1[kkk] := -array_tmp5_a1[kkk-1] * array_tmp4[2] * (kkk-2) / array_tmp2[1] / (kkk - 1); > array_tmp5_a2[kkk-1] := (array_tmp5_a1[kkk-1] * array_tmp4[2] + array_tmp5_a1[kkk] * array_tmp4[1]) * (kkk-1) / glob_h; > array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1)*glob_h/(kkk-1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp6[kkk] := array_tmp5[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_tmp6[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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, 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] := array_const_0D2[1]*array_x[1]; array_tmp4[1] := array_tmp3[1] + array_const_0D3[1]; array_tmp5[1] := expt(array_tmp2[1], array_tmp4[1]); array_tmp5_a1[1] := ln(array_tmp2[1]); array_tmp5_a1[2] := array_tmp2[2]/array_tmp2[1]; array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp6[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_const_0D2[1]*array_x[2]; array_tmp4[2] := array_tmp3[2]; array_tmp5_a2[1] := ( array_tmp5_a1[1]*array_tmp4[2] + array_tmp5_a1[2]*array_tmp4[1])/ glob_h; array_tmp5[2] := array_tmp5[1]*array_tmp5_a2[1]*glob_h; array_tmp6[2] := array_tmp5[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp6[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_tmp5_a1[3] := -1/2*array_tmp5_a1[2]*array_tmp2[2]/array_tmp2[1]; array_tmp5_a2[2] := 2* (array_tmp5_a1[2]*array_tmp4[2] + array_tmp5_a1[3]*array_tmp4[1])/ glob_h; array_tmp5[3] := 1/2*ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[3] := array_tmp5[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp6[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_tmp5_a1[4] := -2/3*array_tmp5_a1[3]*array_tmp2[2]/array_tmp2[1]; array_tmp5_a2[3] := 3* (array_tmp5_a1[3]*array_tmp4[2] + array_tmp5_a1[4]*array_tmp4[1])/ glob_h; array_tmp5[4] := 1/3*ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[4] := array_tmp5[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp6[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_tmp5_a1[5] := -3/4*array_tmp5_a1[4]*array_tmp2[2]/array_tmp2[1]; array_tmp5_a2[4] := 4* (array_tmp5_a1[4]*array_tmp4[2] + array_tmp5_a1[5]*array_tmp4[1])/ glob_h; array_tmp5[5] := 1/4*ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[5] := array_tmp5[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp6[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_tmp5_a1[kkk] := -array_tmp5_a1[kkk - 1]*array_tmp4[2]* (kkk - 2)/(array_tmp2[1]*(kkk - 1)); array_tmp5_a2[kkk - 1] := (array_tmp5_a1[kkk - 1]*array_tmp4[2] + array_tmp5_a1[kkk]*array_tmp4[1])*(kkk - 1)/glob_h; array_tmp5[kkk] := ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/(kkk - 1); array_tmp6[kkk] := array_tmp5[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_tmp6[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(0.0 ) ; > end; exact_soln_y := proc(x) return 0. end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/expt_lin_linpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(0.0 ) ;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5_c1:= Array(0..(max_terms + 1),[]); > array_tmp5_a1:= Array(0..(max_terms + 1),[]); > array_tmp5_a2:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= 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[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_a2[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_tmp6[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 := 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_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_a2[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_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp6[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_const_0D3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D3[1] := 0.3; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T01:20:50-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_lin_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"expt_lin_lin diffeq.mxt") > ; > logitem_str(html_log_file,"expt_lin_lin 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_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/expt_lin_linpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(0.0 ) ;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5_c1 := Array(0 .. max_terms + 1, []); array_tmp5_a1 := Array(0 .. max_terms + 1, []); array_tmp5_a2 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := 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[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_c1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_a2[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_tmp6[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 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_c1[term] := 0.; term := term + 1 end do; array_tmp5_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_a1[term] := 0.; term := term + 1 end do; array_tmp5_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_a2[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_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[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_const_0D3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D3[term] := 0.; term := term + 1 end do; array_const_0D3[1] := 0.3; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T01:20:50-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_lin_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = expt((0.1 * \ x + 0.2) , (0.2 * x + 0.3));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "expt_lin_lin diffeq.mxt"); logitem_str(html_log_file, "expt_lin_lin maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/expt_lin_linpostode.ode################# diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(0.0 ) ; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 4.9 estimated_steps = 4900000 step_error = 2.0408163265306122448979591836735e-17 est_needed_step_err = 2.0408163265306122448979591836735e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.4344981665902949603036122703651e-196 estimated_step_error = 3.4344981665902949603036122703651e-196 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.8889630804708215156296805510342e-155 estimated_step_error = 7.8889630804708215156296805510342e-155 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 = 5.2941888228882317422471966437998e-147 estimated_step_error = 5.2941888228882317422471966437998e-147 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.5528636932729090382664689101979e-139 estimated_step_error = 3.5528636932729090382664689101979e-139 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.3842780301188516281047131185572e-131 estimated_step_error = 2.3842780301188516281047131185572e-131 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6000505809390507879004397042175e-123 estimated_step_error = 1.6000505809390507879004397042175e-123 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0737605756059140680118574323109e-115 estimated_step_error = 1.0737605756059140680118574323109e-115 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 = 7.2056813395662606512729615043512e-108 estimated_step_error = 7.2056813395662606512729615043512e-108 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.8353772382574764555876191820193e-100 estimated_step_error = 4.8353772382574764555876191820193e-100 best_h = 0.000512 opt_iter = 10 bytes used=4000252, alloc=3014104, time=0.12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.2445995074996670632988895553425e-92 estimated_step_error = 3.2445995074996670632988895553425e-92 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1769211546853024359606276156794e-84 estimated_step_error = 2.1769211546853024359606276156794e-84 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4602461952888146354992092175540e-76 estimated_step_error = 1.4602461952888146354992092175540e-76 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 = 9.7906884920338036884879736838536e-69 estimated_step_error = 9.7906884920338036884879736838536e-69 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 = 6.5585635031589350694959844271618e-61 estimated_step_error = 6.5585635031589350694959844271618e-61 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.3855513391997814892455661765302e-53 estimated_step_error = 4.3855513391997814892455661765302e-53 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.9220861982860473282019531979045e-45 estimated_step_error = 2.9220861982860473282019531979045e-45 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9334111586478532343541342645598e-37 estimated_step_error = 1.9334111586478532343541342645598e-37 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2621755102892284966377549473513e-29 estimated_step_error = 1.2621755102892284966377549473513e-29 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0 y[1] (numeric) = 0.0061204845427376375559001978568783 absolute error = 0.0061204845427376375559001978568783 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.151 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.454 Order of pole (six term test) = -0.8616 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0 y[1] (numeric) = 0.012174945832448542362009098003338 absolute error = 0.012174945832448542362009098003338 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.156 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.462 Order of pole (six term test) = -0.8606 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0 y[1] (numeric) = 0.018219884635457830531736587481055 absolute error = 0.018219884635457830531736587481055 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.162 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.47 Order of pole (six term test) = -0.8596 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0 y[1] (numeric) = 0.024255386099563737492822252172528 absolute error = 0.024255386099563737492822252172528 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.167 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.478 Order of pole (six term test) = -0.8587 TOP MAIN SOLVE Loop bytes used=8001340, alloc=4062488, time=0.26 x[1] = 0.15 y[1] (analytic) = 0 y[1] (numeric) = 0.03028153462997530237106722797931 absolute error = 0.03028153462997530237106722797931 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.173 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 = 1.486 Order of pole (six term test) = -0.8577 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0 y[1] (numeric) = 0.036298413899428191665096646543569 absolute error = 0.036298413899428191665096646543569 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.178 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 = 1.494 Order of pole (six term test) = -0.8567 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0 y[1] (numeric) = 0.042306106858126130131511793191383 absolute error = 0.042306106858126130131511793191383 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.184 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 = 1.502 Order of pole (six term test) = -0.8557 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0 y[1] (numeric) = 0.048304695743511707022815587919666 absolute error = 0.048304695743511707022815587919666 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.189 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 = 1.509 Order of pole (six term test) = -0.8548 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0 y[1] (numeric) = 0.054294262089870227919632033960384 absolute error = 0.054294262089870227919632033960384 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.195 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 = 1.517 Order of pole (six term test) = -0.8539 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.060274886737770187477885010166921 absolute error = 0.060274886737770187477885010166921 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.2 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 = 1.525 Order of pole (six term test) = -0.8529 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0 y[1] (numeric) = 0.066246649843343846366743006848599 absolute error = 0.066246649843343846366743006848599 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.206 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 = 1.533 Order of pole (six term test) = -0.852 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0 y[1] (numeric) = 0.072209630887411306404355814141878 absolute error = 0.072209630887411306404355814141878 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.211 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 = 1.541 Order of pole (six term test) = -0.8511 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0 y[1] (numeric) = 0.078163908684451391309702232234473 absolute error = 0.078163908684451391309702232234473 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.217 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.549 Order of pole (six term test) = -0.8502 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0 y[1] (numeric) = 0.084109561391422556487973312004542 absolute error = 0.084109561391422556487973312004542 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.222 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 = 1.557 Order of pole (six term test) = -0.8493 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0 y[1] (numeric) = 0.090046666516436969765153109245627 absolute error = 0.090046666516436969765153109245627 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.228 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.564 Order of pole (six term test) = -0.8484 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0 y[1] (numeric) = 0.095975300927290825899574438951034 absolute error = 0.095975300927290825899574438951034 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.233 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.572 Order of pole (six term test) = -0.8475 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0 y[1] (numeric) = 0.10189554085985388094224572898762 absolute error = 0.10189554085985388094224572898762 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.239 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.58 Order of pole (six term test) = -0.8467 bytes used=12002956, alloc=4324584, time=0.39 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0 y[1] (numeric) = 0.10780746192632111801483067539425 absolute error = 0.10780746192632111801483067539425 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.244 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.588 Order of pole (six term test) = -0.8458 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0 y[1] (numeric) = 0.11371113912332938374848398951953 absolute error = 0.11371113912332938374848398951953 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.596 Order of pole (six term test) = -0.845 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.11960664683994176440535078871432 absolute error = 0.11960664683994176440535078871432 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.255 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.604 Order of pole (six term test) = -0.8441 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0 y[1] (numeric) = 0.12549405886550240251722702210419 absolute error = 0.12549405886550240251722702210419 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.261 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.611 Order of pole (six term test) = -0.8433 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0 y[1] (numeric) = 0.1313734483973643886550970268604 absolute error = 0.1313734483973643886550970268604 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.266 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.619 Order of pole (six term test) = -0.8425 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0 y[1] (numeric) = 0.13724488804849329862398506585065 absolute error = 0.13724488804849329862398506585065 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.272 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 = 1.627 Order of pole (six term test) = -0.8417 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0 y[1] (numeric) = 0.14310844985494888389717820055947 absolute error = 0.14310844985494888389717820055947 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.277 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.635 Order of pole (six term test) = -0.8408 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0 y[1] (numeric) = 0.14896420528324736240211974575776 absolute error = 0.14896420528324736240211974575776 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.283 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 = 1.643 Order of pole (six term test) = -0.84 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0 y[1] (numeric) = 0.15481222523760669778908544958739 absolute error = 0.15481222523760669778908544958739 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.288 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.651 Order of pole (six term test) = -0.8393 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0 y[1] (numeric) = 0.16065258006707719799722442043435 absolute error = 0.16065258006707719799722442043435 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.294 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 = 1.658 Order of pole (six term test) = -0.8385 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0 y[1] (numeric) = 0.16648533957255970822680854987937 absolute error = 0.16648533957255970822680854987937 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.299 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.666 Order of pole (six term test) = -0.8377 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0 y[1] (numeric) = 0.17231057301371361927968799589308 absolute error = 0.17231057301371361927968799589308 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.305 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 = 1.674 Order of pole (six term test) = -0.8369 TOP MAIN SOLVE Loop bytes used=16003740, alloc=4390108, time=0.53 x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.17812834911575685959198201628797 absolute error = 0.17812834911575685959198201628797 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.682 Order of pole (six term test) = -0.8362 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0 y[1] (numeric) = 0.18393873607615998810573927429558 absolute error = 0.18393873607615998810573927429558 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.315 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.69 Order of pole (six term test) = -0.8354 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0 y[1] (numeric) = 0.18974180157123645536321141589686 absolute error = 0.18974180157123645536321141589686 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.321 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.697 Order of pole (six term test) = -0.8347 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0 y[1] (numeric) = 0.19553761276263105181369692635332 absolute error = 0.19553761276263105181369692635332 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.326 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 = 1.705 Order of pole (six term test) = -0.8339 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0 y[1] (numeric) = 0.20132623630370851525542810890221 absolute error = 0.20132623630370851525542810890221 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.332 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 = 1.713 Order of pole (six term test) = -0.8332 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0 y[1] (numeric) = 0.20710773834584422355202839427423 absolute error = 0.20710773834584422355202839427423 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.337 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 = 1.721 Order of pole (six term test) = -0.8325 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0 y[1] (numeric) = 0.2128821845446188542244719664523 absolute error = 0.2128821845446188542244719664523 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.343 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 = 1.729 Order of pole (six term test) = -0.8317 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0 y[1] (numeric) = 0.21864964006591884918646256023039 absolute error = 0.21864964006591884918646256023039 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.348 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 = 1.736 Order of pole (six term test) = -0.831 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0 y[1] (numeric) = 0.22441016959194448072630508004341 absolute error = 0.22441016959194448072630508004341 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.354 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 = 1.744 Order of pole (six term test) = -0.8303 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0 y[1] (numeric) = 0.23016383732712727380557313656265 absolute error = 0.23016383732712727380557313656265 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.359 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 = 1.752 Order of pole (six term test) = -0.8296 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.23591070700395849980933636780007 absolute error = 0.23591070700395849980933636780007 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.365 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 = 1.76 Order of pole (six term test) = -0.8289 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0 y[1] (numeric) = 0.24165084188873041801077134110824 absolute error = 0.24165084188873041801077134110824 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.37 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 = 1.767 Order of pole (six term test) = -0.8282 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0 y[1] (numeric) = 0.24738430478719190317216923042169 absolute error = 0.24738430478719190317216923042169 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.376 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 = 1.775 Order of pole (six term test) = -0.8276 TOP MAIN SOLVE Loop bytes used=20004828, alloc=4455632, time=0.67 x[1] = 0.53 y[1] (analytic) = 0 y[1] (numeric) = 0.25311115805012006086332040226605 absolute error = 0.25311115805012006086332040226605 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.381 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.783 Order of pole (six term test) = -0.8269 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0 y[1] (numeric) = 0.25883146357880939620672354513457 absolute error = 0.25883146357880939620672354513457 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.387 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.791 Order of pole (six term test) = -0.8262 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0 y[1] (numeric) = 0.26454528283048006682779199717001 absolute error = 0.26454528283048006682779199717001 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.392 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.798 Order of pole (six term test) = -0.8256 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0 y[1] (numeric) = 0.27025267682360671676896407185829 absolute error = 0.27025267682360671676896407185829 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.398 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.806 Order of pole (six term test) = -0.8249 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0 y[1] (numeric) = 0.27595370614316935499207605795083 absolute error = 0.27595370614316935499207605795083 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.403 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.814 Order of pole (six term test) = -0.8242 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0 y[1] (numeric) = 0.28164843094582770981715571020229 absolute error = 0.28164843094582770981715571020229 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.409 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.822 Order of pole (six term test) = -0.8236 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0 y[1] (numeric) = 0.28733691096502045920245632834803 absolute error = 0.28733691096502045920245632834803 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.414 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.83 Order of pole (six term test) = -0.823 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.29301920551599070613544601311239 absolute error = 0.29301920551599070613544601311239 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.837 Order of pole (six term test) = -0.8223 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0 y[1] (numeric) = 0.29869537350073903855378386723711 absolute error = 0.29869537350073903855378386723711 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.425 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.845 Order of pole (six term test) = -0.8217 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0 y[1] (numeric) = 0.30436547341290548412603617841879 absolute error = 0.30436547341290548412603617841879 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.431 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 = 1.853 Order of pole (six term test) = -0.8211 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0 y[1] (numeric) = 0.31002956334258164187175406862758 absolute error = 0.31002956334258164187175406862758 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.436 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.861 Order of pole (six term test) = -0.8205 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0 y[1] (numeric) = 0.31568770098105424496802644891696 absolute error = 0.31568770098105424496802644891696 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.442 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 = 1.868 Order of pole (six term test) = -0.8199 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0 y[1] (numeric) = 0.32133994362548138215392183747686 absolute error = 0.32133994362548138215392183747686 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.447 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 = 1.876 Order of pole (six term test) = -0.8193 TOP MAIN SOLVE Loop bytes used=24006144, alloc=4455632, time=0.80 x[1] = 0.66 y[1] (analytic) = 0 y[1] (numeric) = 0.32698634818350257888520404269158 absolute error = 0.32698634818350257888520404269158 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.453 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 = 1.884 Order of pole (six term test) = -0.8187 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0 y[1] (numeric) = 0.33262697117778391378987036272055 absolute error = 0.33262697117778391378987036272055 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.458 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 = 1.892 Order of pole (six term test) = -0.8181 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0 y[1] (numeric) = 0.33826186875049932101156961581495 absolute error = 0.33826186875049932101156961581495 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.464 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 = 1.899 Order of pole (six term test) = -0.8175 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0 y[1] (numeric) = 0.34389109666774920468457328278079 absolute error = 0.34389109666774920468457328278079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.469 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 = 1.907 Order of pole (six term test) = -0.8169 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.34951471032391746804304615660381 absolute error = 0.34951471032391746804304615660381 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.474 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.915 Order of pole (six term test) = -0.8164 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0 y[1] (numeric) = 0.35513276474596803651180948146586 absolute error = 0.35513276474596803651180948146586 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.48 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 = 1.923 Order of pole (six term test) = -0.8158 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0 y[1] (numeric) = 0.36074531459768193153907220309494 absolute error = 0.36074531459768193153907220309494 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.485 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 = 1.93 Order of pole (six term test) = -0.8152 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0 y[1] (numeric) = 0.36635241418383592989771403719095 absolute error = 0.36635241418383592989771403719095 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.491 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.938 Order of pole (six term test) = -0.8147 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0 y[1] (numeric) = 0.3719541174543238216851351223505 absolute error = 0.3719541174543238216851351223505 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.496 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 = 1.946 Order of pole (six term test) = -0.8141 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0 y[1] (numeric) = 0.37755047800822125927742877792644 absolute error = 0.37755047800822125927742877792644 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.502 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 = 1.953 Order of pole (six term test) = -0.8136 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0 y[1] (numeric) = 0.38314154909779516902714699505441 absolute error = 0.38314154909779516902714699505441 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.507 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 = 1.961 Order of pole (six term test) = -0.813 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0 y[1] (numeric) = 0.38872738363245867752112976875867 absolute error = 0.38872738363245867752112976875867 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.513 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 = 1.969 Order of pole (six term test) = -0.8125 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0 y[1] (numeric) = 0.3943080341826724847221166660382 absolute error = 0.3943080341826724847221166660382 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.518 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 = 1.977 Order of pole (six term test) = -0.812 bytes used=28009588, alloc=4455632, time=0.95 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0 y[1] (numeric) = 0.39988355298379359729193464364837 absolute error = 0.39988355298379359729193464364837 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.524 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 = 1.984 Order of pole (six term test) = -0.8114 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0 y[1] (numeric) = 0.4054539919398723168221529526631 absolute error = 0.4054539919398723168221529526631 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.529 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.992 Order of pole (six term test) = -0.8109 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0 y[1] (numeric) = 0.41101940262739835956780303768823 absolute error = 0.41101940262739835956780303768823 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.535 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 = 2 Order of pole (six term test) = -0.8104 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0 y[1] (numeric) = 0.41657983629899696657905023106338 absolute error = 0.41657983629899696657905023106338 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.008 Order of pole (six term test) = -0.8099 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0 y[1] (numeric) = 0.42213534388707584584291574043743 absolute error = 0.42213534388707584584291574043743 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.546 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 = 2.015 Order of pole (six term test) = -0.8094 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0 y[1] (numeric) = 0.42768597600742377117097969908559 absolute error = 0.42768597600742377117097969908559 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.551 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.023 Order of pole (six term test) = -0.8089 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0 y[1] (numeric) = 0.43323178296276164608849129203172 absolute error = 0.43323178296276164608849129203172 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.557 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.031 Order of pole (six term test) = -0.8084 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0 y[1] (numeric) = 0.43877281474624682488484552426931 absolute error = 0.43877281474624682488484552426931 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.562 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.038 Order of pole (six term test) = -0.8079 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0 y[1] (numeric) = 0.44430912104493146726465507561653 absolute error = 0.44430912104493146726465507561653 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.568 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.046 Order of pole (six term test) = -0.8074 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0 y[1] (numeric) = 0.44984075124317568768265774493148 absolute error = 0.44984075124317568768265774493148 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.573 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.054 Order of pole (six term test) = -0.8069 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0 y[1] (numeric) = 0.45536775442601624544476348189246 absolute error = 0.45536775442601624544476348189246 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.579 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.062 Order of pole (six term test) = -0.8064 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0 y[1] (numeric) = 0.46089017938249150700225854587427 absolute error = 0.46089017938249150700225854587427 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.584 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.069 Order of pole (six term test) = -0.806 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0 y[1] (numeric) = 0.4664080746089233975474271975165 absolute error = 0.4664080746089233975474271975165 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=32010260, alloc=4521156, time=1.09 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.59 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 = 2.077 Order of pole (six term test) = -0.8055 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0 y[1] (numeric) = 0.47192148831215704502777414313521 absolute error = 0.47192148831215704502777414313521 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.595 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 = 2.085 Order of pole (six term test) = -0.805 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0 y[1] (numeric) = 0.47743046841275880602404669948257 absolute error = 0.47743046841275880602404669948257 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.601 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 = 2.093 Order of pole (six term test) = -0.8046 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0 y[1] (numeric) = 0.48293506254817334957603101462252 absolute error = 0.48293506254817334957603101462252 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.606 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 = 2.1 Order of pole (six term test) = -0.8041 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0 y[1] (numeric) = 0.48843531807584046198154371954755 absolute error = 0.48843531807584046198154371954755 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.612 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 = 2.108 Order of pole (six term test) = -0.8037 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0 y[1] (numeric) = 0.49393128207627222283030846567887 absolute error = 0.49393128207627222283030846567887 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.617 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 = 2.116 Order of pole (six term test) = -0.8032 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0 y[1] (numeric) = 0.499423001356091190057874867945 absolute error = 0.499423001356091190057874867945 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.622 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.123 Order of pole (six term test) = -0.8028 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0 y[1] (numeric) = 0.50491052245103021960800646401744 absolute error = 0.50491052245103021960800646401744 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.628 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 = 2.131 Order of pole (six term test) = -0.8023 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0 y[1] (numeric) = 0.51039389162889453336785035607535 absolute error = 0.51039389162889453336785035607535 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.633 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.139 Order of pole (six term test) = -0.8019 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0 y[1] (numeric) = 0.51587315489248663738172811067429 absolute error = 0.51587315489248663738172811067429 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.639 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 = 2.147 Order of pole (six term test) = -0.8015 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0 y[1] (numeric) = 0.52134835798249468094978039422195 absolute error = 0.52134835798249468094978039422195 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.644 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 = 2.154 Order of pole (six term test) = -0.801 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0 y[1] (numeric) = 0.52681954638034483607037664487638 absolute error = 0.52681954638034483607037664487638 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.162 Order of pole (six term test) = -0.8006 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0 y[1] (numeric) = 0.53228676531101826578377431136566 absolute error = 0.53228676531101826578377431136566 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.655 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 = 2.17 Order of pole (six term test) = -0.8002 TOP MAIN SOLVE Loop bytes used=36011316, alloc=4521156, time=1.23 x[1] = 1.04 y[1] (analytic) = 0 y[1] (numeric) = 0.53775005974583323931277085319988 absolute error = 0.53775005974583323931277085319988 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.661 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.177 Order of pole (six term test) = -0.7998 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0 y[1] (numeric) = 0.54320947440519294146800356364331 absolute error = 0.54320947440519294146800356364331 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.666 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 = 2.185 Order of pole (six term test) = -0.7994 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0 y[1] (numeric) = 0.54866505376129951358525625687168 absolute error = 0.54866505376129951358525625687168 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.672 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.193 Order of pole (six term test) = -0.799 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0 y[1] (numeric) = 0.55411684204083485328393260199119 absolute error = 0.55411684204083485328393260199119 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.677 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 = 2.201 Order of pole (six term test) = -0.7986 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0 y[1] (numeric) = 0.55956488322760869057421855897659 absolute error = 0.55956488322760869057421855897659 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.208 Order of pole (six term test) = -0.7982 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0 y[1] (numeric) = 0.56500922106517444829000163178472 absolute error = 0.56500922106517444829000163178472 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.688 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.216 Order of pole (six term test) = -0.7978 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.57044989905941338548011378414486 absolute error = 0.57044989905941338548011378414486 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.694 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.224 Order of pole (six term test) = -0.7974 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0 y[1] (numeric) = 0.5758869604810875132468350777286 absolute error = 0.5758869604810875132468350777286 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.699 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.231 Order of pole (six term test) = -0.797 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0 y[1] (numeric) = 0.58132044836836176357289500338014 absolute error = 0.58132044836836176357289500338014 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.705 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.239 Order of pole (six term test) = -0.7966 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0 y[1] (numeric) = 0.58675040552929588292163371783758 absolute error = 0.58675040552929588292163371783758 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.247 Order of pole (six term test) = -0.7962 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0 y[1] (numeric) = 0.59217687454430651382486439758973 absolute error = 0.59217687454430651382486439758973 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.716 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 = 2.255 Order of pole (six term test) = -0.7959 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 0 y[1] (numeric) = 0.59759989776859991928476781280392 absolute error = 0.59759989776859991928476781280392 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.721 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.262 Order of pole (six term test) = -0.7955 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0 y[1] (numeric) = 0.60301951733457579660543290375159 absolute error = 0.60301951733457579660543290375159 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.727 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 = 2.27 Order of pole (six term test) = -0.7951 TOP MAIN SOLVE Loop bytes used=40012252, alloc=4521156, time=1.37 x[1] = 1.17 y[1] (analytic) = 0 y[1] (numeric) = 0.60843577515420261923213545433232 absolute error = 0.60843577515420261923213545433232 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.732 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.278 Order of pole (six term test) = -0.7948 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0 y[1] (numeric) = 0.61384871292136493730794101017802 absolute error = 0.61384871292136493730794101017802 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.738 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 = 2.285 Order of pole (six term test) = -0.7944 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0 y[1] (numeric) = 0.61925837211418305995366179279409 absolute error = 0.61925837211418305995366179279409 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.743 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 = 2.293 Order of pole (six term test) = -0.794 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 0.62466479399730553473463458692124 absolute error = 0.62466479399730553473463458692124 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.749 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 = 2.301 Order of pole (six term test) = -0.7937 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0 y[1] (numeric) = 0.63006801962417483239236842937904 absolute error = 0.63006801962417483239236842937904 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.754 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 = 2.309 Order of pole (six term test) = -0.7933 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0 y[1] (numeric) = 0.63546808983926663768709212385878 absolute error = 0.63546808983926663768709212385878 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.759 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.316 Order of pole (six term test) = -0.793 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0 y[1] (numeric) = 0.64086504528030314011496747323405 absolute error = 0.64086504528030314011496747323405 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.765 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 = 2.324 Order of pole (six term test) = -0.7926 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0 y[1] (numeric) = 0.64625892638044071132767758322071 absolute error = 0.64625892638044071132767758322071 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.332 Order of pole (six term test) = -0.7923 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0 y[1] (numeric) = 0.65164977337043234928879826294063 absolute error = 0.65164977337043234928879826294063 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.776 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 = 2.34 Order of pole (six term test) = -0.792 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0 y[1] (numeric) = 0.65703762628076526254745392042456 absolute error = 0.65703762628076526254745392042456 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.781 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.347 Order of pole (six term test) = -0.7916 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0 y[1] (numeric) = 0.66242252494377396149197607163832 absolute error = 0.66242252494377396149197607163832 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.787 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 = 2.355 Order of pole (six term test) = -0.7913 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0 y[1] (numeric) = 0.66780450899572921706143782130104 absolute error = 0.66780450899572921706143782130104 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.792 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.363 Order of pole (six term test) = -0.791 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0 y[1] (numeric) = 0.67318361787890324113793058074663 absolute error = 0.67318361787890324113793058074663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.798 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.37 Order of pole (six term test) = -0.7907 TOP MAIN SOLVE Loop bytes used=44014828, alloc=4521156, time=1.51 x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 0.67855989084361143671426052349733 absolute error = 0.67855989084361143671426052349733 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.803 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 = 2.378 Order of pole (six term test) = -0.7903 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0 y[1] (numeric) = 0.68393336695023105992743163269174 absolute error = 0.68393336695023105992743163269174 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.809 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.386 Order of pole (six term test) = -0.79 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0 y[1] (numeric) = 0.68930408507119713016498627646673 absolute error = 0.68930408507119713016498627646673 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.814 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 = 2.394 Order of pole (six term test) = -0.7897 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0 y[1] (numeric) = 0.69467208389297591868620425550978 absolute error = 0.69467208389297591868620425550978 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.401 Order of pole (six term test) = -0.7894 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0 y[1] (numeric) = 0.70003740191801634055060082415675 absolute error = 0.70003740191801634055060082415675 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.825 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 = 2.409 Order of pole (six term test) = -0.7891 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0 y[1] (numeric) = 0.7054000774666795691094672476728 absolute error = 0.7054000774666795691094672476728 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.831 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.417 Order of pole (six term test) = -0.7888 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0 y[1] (numeric) = 0.7107601486791471868897862845512 absolute error = 0.7107601486791471868897862845512 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.836 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 = 2.424 Order of pole (six term test) = -0.7885 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0 y[1] (numeric) = 0.71611765351730818138121817827948 absolute error = 0.71611765351730818138121817827948 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.842 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.432 Order of pole (six term test) = -0.7882 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0 y[1] (numeric) = 0.72147262976662508902354335614623 absolute error = 0.72147262976662508902354335614623 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.847 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 = 2.44 Order of pole (six term test) = -0.7879 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0 y[1] (numeric) = 0.72682511503797958558158171487872 absolute error = 0.72682511503797958558158171487872 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.853 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 = 2.448 Order of pole (six term test) = -0.7876 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 0.73217514676949781608486159703212 absolute error = 0.73217514676949781608486159703212 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.858 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.455 Order of pole (six term test) = -0.7873 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0 y[1] (numeric) = 0.73752276222835575259791989577921 absolute error = 0.73752276222835575259791989577921 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.864 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 = 2.463 Order of pole (six term test) = -0.787 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0 y[1] (numeric) = 0.74286799851256486327187115920847 absolute error = 0.74286799851256486327187115920847 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.869 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.471 Order of pole (six term test) = -0.7868 TOP MAIN SOLVE Loop bytes used=48016652, alloc=4521156, time=1.65 x[1] = 1.43 y[1] (analytic) = 0 y[1] (numeric) = 0.74821089255273837140663689072559 absolute error = 0.74821089255273837140663689072559 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.875 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 = 2.479 Order of pole (six term test) = -0.7865 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0 y[1] (numeric) = 0.75355148111383837862387948418856 absolute error = 0.75355148111383837862387948418856 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.486 Order of pole (six term test) = -0.7862 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0 y[1] (numeric) = 0.75888980079690412171119412643947 absolute error = 0.75888980079690412171119412643947 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.886 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 = 2.494 Order of pole (six term test) = -0.7859 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0 y[1] (numeric) = 0.7642258880407616282464835180027 absolute error = 0.7642258880407616282464835180027 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.891 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.502 Order of pole (six term test) = -0.7857 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 0 y[1] (numeric) = 0.769559779123715031745731184715 absolute error = 0.769559779123715031745731184715 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.896 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.51 Order of pole (six term test) = -0.7854 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0 y[1] (numeric) = 0.77489151016521980279570468148905 absolute error = 0.77489151016521980279570468148905 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.902 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 = 2.517 Order of pole (six term test) = -0.7851 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0 y[1] (numeric) = 0.78022111712753814843361240698176 absolute error = 0.78022111712753814843361240698176 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.907 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.525 Order of pole (six term test) = -0.7849 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 0.78554863581737682791660511588402 absolute error = 0.78554863581737682791660511588402 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.913 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.533 Order of pole (six term test) = -0.7846 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 0 y[1] (numeric) = 0.79087410188750762898349811169015 absolute error = 0.79087410188750762898349811169015 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.918 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.54 Order of pole (six term test) = -0.7844 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0 y[1] (numeric) = 0.79619755083837074474747839788793 absolute error = 0.79619755083837074474747839788793 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.924 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.548 Order of pole (six term test) = -0.7841 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 0 y[1] (numeric) = 0.80151901801966128747018073658573 absolute error = 0.80151901801966128747018073658573 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.929 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.556 Order of pole (six term test) = -0.7839 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0 y[1] (numeric) = 0.80683853863189917165273654322496 absolute error = 0.80683853863189917165273654322496 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.935 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.564 Order of pole (six term test) = -0.7836 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0 y[1] (numeric) = 0.81215614772798259513662860612714 absolute error = 0.81215614772798259513662860612714 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.571 Order of pole (six term test) = -0.7834 bytes used=52018224, alloc=4521156, time=1.79 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 0 y[1] (numeric) = 0.81747188021472534323487028879657 absolute error = 0.81747188021472534323487028879657 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.946 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 = 2.579 Order of pole (six term test) = -0.7831 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0 y[1] (numeric) = 0.82278577085437813731065538617117 absolute error = 0.82278577085437813731065538617117 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.951 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.587 Order of pole (six term test) = -0.7829 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0 y[1] (numeric) = 0.82809785426613424568471608592541 absolute error = 0.82809785426613424568471608592541 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.957 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.595 Order of pole (six term test) = -0.7827 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 0 y[1] (numeric) = 0.83340816492761957128273915393346 absolute error = 0.83340816492761957128273915393346 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.962 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.602 Order of pole (six term test) = -0.7824 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 0.83871673717636742702891688020551 absolute error = 0.83871673717636742702891688020551 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.968 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.61 Order of pole (six term test) = -0.7822 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0 y[1] (numeric) = 0.84402360521127820664967565790212 absolute error = 0.84402360521127820664967565790212 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.973 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 = 2.618 Order of pole (six term test) = -0.782 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0 y[1] (numeric) = 0.84932880309406415527149039867287 absolute error = 0.84932880309406415527149039867287 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.979 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.626 Order of pole (six term test) = -0.7818 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0 y[1] (numeric) = 0.85463236475067944097714841637085 absolute error = 0.85463236475067944097714841637085 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.984 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 = 2.633 Order of pole (six term test) = -0.7815 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0 y[1] (numeric) = 0.85993432397273572532459421944062 absolute error = 0.85993432397273572532459421944062 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.641 Order of pole (six term test) = -0.7813 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0 y[1] (numeric) = 0.86523471441890342773031947251716 absolute error = 0.86523471441890342773031947251716 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.995 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 = 2.649 Order of pole (six term test) = -0.7811 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0 y[1] (numeric) = 0.8705335696162988755739424017593 absolute error = 0.8705335696162988755739424017593 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.001 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.657 Order of pole (six term test) = -0.7809 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 0 y[1] (numeric) = 0.87583092296185752889095907839214 absolute error = 0.87583092296185752889095907839214 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.006 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 = 2.664 Order of pole (six term test) = -0.7807 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0 y[1] (numeric) = 0.88112680772369346558548428739803 absolute error = 0.88112680772369346558548428739803 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.012 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 = 2.672 Order of pole (six term test) = -0.7805 bytes used=56020728, alloc=4586680, time=1.93 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0 y[1] (numeric) = 0.88642125704244531021299831990701 absolute error = 0.88642125704244531021299831990701 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.017 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.68 Order of pole (six term test) = -0.7803 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 0.89171430393260878655357083224912 absolute error = 0.89171430393260878655357083224912 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.023 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 = 2.688 Order of pole (six term test) = -0.7801 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0 y[1] (numeric) = 0.89700598128385607141766257998917 absolute error = 0.89700598128385607141766257998917 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.028 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.695 Order of pole (six term test) = -0.7799 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0 y[1] (numeric) = 0.90229632186234212439835425155191 absolute error = 0.90229632186234212439835425155191 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.034 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 = 2.703 Order of pole (six term test) = -0.7797 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0 y[1] (numeric) = 0.90758535831199816560468723168726 absolute error = 0.90758535831199816560468723168726 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.039 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.711 Order of pole (six term test) = -0.7795 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0 y[1] (numeric) = 0.91287312315581247077971627214481 absolute error = 0.91287312315581247077971627214481 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.044 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.719 Order of pole (six term test) = -0.7793 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0 y[1] (numeric) = 0.91815964879709865062288438467901 absolute error = 0.91815964879709865062288438467901 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.727 Order of pole (six term test) = -0.7791 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0 y[1] (numeric) = 0.92344496752075157859847414692112 absolute error = 0.92344496752075157859847414692112 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.055 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.734 Order of pole (six term test) = -0.7789 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0 y[1] (numeric) = 0.92872911149449112901922748744565 absolute error = 0.92872911149449112901922748744565 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.061 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 = 2.742 Order of pole (six term test) = -0.7787 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0 y[1] (numeric) = 0.93401211277009388474583990518477 absolute error = 0.93401211277009388474583990518477 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.066 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 = 2.75 Order of pole (six term test) = -0.7786 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0 y[1] (numeric) = 0.93929400328461297143802799299501 absolute error = 0.93929400328461297143802799299501 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.072 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 = 2.758 Order of pole (six term test) = -0.7784 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 0.94457481486158617293036455421993 absolute error = 0.94457481486158617293036455421993 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.077 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 = 2.765 Order of pole (six term test) = -0.7782 TOP MAIN SOLVE Loop bytes used=60021420, alloc=4586680, time=2.07 x[1] = 1.81 y[1] (analytic) = 0 y[1] (numeric) = 0.94985457921223247998521694947014 absolute error = 0.94985457921223247998521694947014 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.083 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 = 2.773 Order of pole (six term test) = -0.778 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0 y[1] (numeric) = 0.9551333279366372223950744550192 absolute error = 0.9551333279366372223950744550192 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.088 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 = 2.781 Order of pole (six term test) = -0.7779 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0 y[1] (numeric) = 0.96041109252492593216649117136289 absolute error = 0.96041109252492593216649117136289 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.094 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 = 2.789 Order of pole (six term test) = -0.7777 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0 y[1] (numeric) = 0.96568790435842708331700268133603 absolute error = 0.96568790435842708331700268133603 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.099 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 = 2.796 Order of pole (six term test) = -0.7775 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 0 y[1] (numeric) = 0.97096379471082385165391552207742 absolute error = 0.97096379471082385165391552207742 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.105 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 = 2.804 Order of pole (six term test) = -0.7774 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0 y[1] (numeric) = 0.97623879474929503577905446295871 absolute error = 0.97623879474929503577905446295871 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.11 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 = 2.812 Order of pole (six term test) = -0.7772 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0 y[1] (numeric) = 0.98151293553564527847563655109743 absolute error = 0.98151293553564527847563655109743 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.116 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.82 Order of pole (six term test) = -0.777 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0 y[1] (numeric) = 0.98678624802742472558169256928921 absolute error = 0.98678624802742472558169256928921 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.121 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.828 Order of pole (six term test) = -0.7769 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0 y[1] (numeric) = 0.99205876307903825743816189854778 absolute error = 0.99205876307903825743816189854778 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.127 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.835 Order of pole (six term test) = -0.7767 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0 y[1] (numeric) = 0.99733051144284442601824761422841 absolute error = 0.99733051144284442601824761422841 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.132 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.843 Order of pole (six term test) = -0.7766 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0 y[1] (numeric) = 1.0026015237702442288971522785761 absolute error = 1.0026015237702442288971522785761 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.138 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.851 Order of pole (six term test) = -0.7764 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 0 y[1] (numeric) = 1.0078718306127598493072537316516 absolute error = 1.0078718306127598493072537316516 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.143 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.859 Order of pole (six term test) = -0.7763 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 0 y[1] (numeric) = 1.0131414624231034896424713641744 absolute error = 1.0131414624231034896424713641744 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.149 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.867 Order of pole (six term test) = -0.7761 TOP MAIN SOLVE Loop bytes used=64022416, alloc=4586680, time=2.22 x[1] = 1.94 y[1] (analytic) = 0 y[1] (numeric) = 1.0184104495562364239263783847763 absolute error = 1.0184104495562364239263783847763 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.154 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.874 Order of pole (six term test) = -0.776 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0 y[1] (numeric) = 1.0236788222704183929409099914037 absolute error = 1.0236788222704183929409099914037 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.882 Order of pole (six term test) = -0.7759 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0 y[1] (numeric) = 1.0289466107282474639256903169314 absolute error = 1.0289466107282474639256903169314 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.165 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.89 Order of pole (six term test) = -0.7757 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0 y[1] (numeric) = 1.0342138449976904750014550781631 absolute error = 1.0342138449976904750014550781631 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.171 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 = 2.898 Order of pole (six term test) = -0.7756 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0 y[1] (numeric) = 1.0394805550531041827441975678686 absolute error = 1.0394805550531041827441975678686 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.176 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.906 Order of pole (six term test) = -0.7754 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0 y[1] (numeric) = 1.0447467707762472296389412454337 absolute error = 1.0447467707762472296389412454337 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.181 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.913 Order of pole (six term test) = -0.7753 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.050012521957283046472883351715 absolute error = 1.050012521957283046472883351715 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.187 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.921 Order of pole (six term test) = -0.7752 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 0 y[1] (numeric) = 1.0552778382957738030865134422076 absolute error = 1.0552778382957738030865134422076 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.192 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.929 Order of pole (six term test) = -0.7751 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0 y[1] (numeric) = 1.0605427494016655192876530489636 absolute error = 1.0605427494016655192876530489636 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.198 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.937 Order of pole (six term test) = -0.7749 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0 y[1] (numeric) = 1.0658072847962644461466639169152 absolute error = 1.0658072847962644461466639169152 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.203 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.945 Order of pole (six term test) = -0.7748 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0 y[1] (numeric) = 1.0710714739132048263308197315096 absolute error = 1.0710714739132048263308197315096 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.209 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.952 Order of pole (six term test) = -0.7747 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0 y[1] (numeric) = 1.0763353460994081406015282566644 absolute error = 1.0763353460994081406015282566644 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.214 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.96 Order of pole (six term test) = -0.7746 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 0 y[1] (numeric) = 1.0815989306160339460892363461146 absolute error = 1.0815989306160339460892363461146 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.968 Order of pole (six term test) = -0.7745 TOP MAIN SOLVE Loop bytes used=68023352, alloc=4586680, time=2.36 x[1] = 2.07 y[1] (analytic) = 0 y[1] (numeric) = 1.086862256639422410476968850156 absolute error = 1.086862256639422410476968850156 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.225 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 = 2.976 Order of pole (six term test) = -0.7743 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0 y[1] (numeric) = 1.0921253532620286447640737004359 absolute error = 1.0921253532620286447640737004359 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.231 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 = 2.984 Order of pole (six term test) = -0.7742 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0 y[1] (numeric) = 1.0973882494933489358464090771959 absolute error = 1.0973882494933489358464090771959 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.236 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 = 2.992 Order of pole (six term test) = -0.7741 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0 y[1] (numeric) = 1.1026509742608389787374639430671 absolute error = 1.1026509742608389787374639430671 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.242 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 = 2.999 Order of pole (six term test) = -0.774 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0 y[1] (numeric) = 1.1079135564108242068663092704286 absolute error = 1.1079135564108242068663092704286 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.247 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 = 3.007 Order of pole (six term test) = -0.7739 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0 y[1] (numeric) = 1.1131760247094023175224021860931 absolute error = 1.1131760247094023175224021860931 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.253 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 = 3.015 Order of pole (six term test) = -0.7738 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0 y[1] (numeric) = 1.1184384078433380881736862663606 absolute error = 1.1184384078433380881736862663606 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.258 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 = 3.023 Order of pole (six term test) = -0.7737 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0 y[1] (numeric) = 1.1237007344209505780627344522918 absolute error = 1.1237007344209505780627344522918 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.264 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 = 3.031 Order of pole (six term test) = -0.7736 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 0 y[1] (numeric) = 1.1289630329729928081854612844759 absolute error = 1.1289630329729928081854612844759 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.269 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.039 Order of pole (six term test) = -0.7735 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0 y[1] (numeric) = 1.1342253319535240114777915927495 absolute error = 1.1342253319535240114777915927495 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.275 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 = 3.046 Order of pole (six term test) = -0.7734 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0 y[1] (numeric) = 1.1394876597407745437772248866639 absolute error = 1.1394876597407745437772248866639 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.054 Order of pole (six term test) = -0.7733 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0 y[1] (numeric) = 1.1447500446380035448880980067848 absolute error = 1.1447500446380035448880980067848 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.286 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.062 Order of pole (six term test) = -0.7732 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0 y[1] (numeric) = 1.1500125148743494378611505213381 absolute error = 1.1500125148743494378611505213381 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.291 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.07 Order of pole (six term test) = -0.7731 TOP MAIN SOLVE Loop bytes used=72024612, alloc=4586680, time=2.50 x[1] = 2.2 y[1] (analytic) = 0 y[1] (numeric) = 1.1552750986056733533993729886446 absolute error = 1.1552750986056733533993729886446 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.297 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.078 Order of pole (six term test) = -0.7731 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0 y[1] (numeric) = 1.160537823915395565122710173042 absolute error = 1.160537823915395565122710173042 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.302 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.086 Order of pole (six term test) = -0.773 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0 y[1] (numeric) = 1.1658007188153250202636495666918 absolute error = 1.1658007188153250202636495666918 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.308 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.094 Order of pole (six term test) = -0.7729 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0 y[1] (numeric) = 1.1710638112464820492237072763315 absolute error = 1.1710638112464820492237072763315 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.313 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.101 Order of pole (six term test) = -0.7728 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0 y[1] (numeric) = 1.1763271290799143362969926419777 absolute error = 1.1763271290799143362969926419777 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.319 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.109 Order of pole (six term test) = -0.7727 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0 y[1] (numeric) = 1.18159070011750623276106087836 absolute error = 1.18159070011750623276106087836 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.324 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.117 Order of pole (six term test) = -0.7727 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0 y[1] (numeric) = 1.186854552092781492446827283741 absolute error = 1.186854552092781492446827283741 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.329 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.125 Order of pole (six term test) = -0.7726 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0 y[1] (numeric) = 1.1921187126716995088281014070801 absolute error = 1.1921187126716995088281014070801 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.335 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 = 3.133 Order of pole (six term test) = -0.7725 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 0 y[1] (numeric) = 1.1973832094534451316169956657351 absolute error = 1.1973832094534451316169956657351 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.141 Order of pole (six term test) = -0.7724 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0 y[1] (numeric) = 1.2026480699712121398137671805724 absolute error = 1.2026480699712121398137671805724 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.346 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 = 3.149 Order of pole (six term test) = -0.7724 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0 y[1] (numeric) = 1.2079133216929804471382670773362 absolute error = 1.2079133216929804471382670773362 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.351 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.156 Order of pole (six term test) = -0.7723 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0 y[1] (numeric) = 1.2131789920222871147648072045124 absolute error = 1.2131789920222871147648072045124 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.357 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 = 3.164 Order of pole (six term test) = -0.7722 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0 y[1] (numeric) = 1.2184451082989912452926249952798 absolute error = 1.2184451082989912452926249952798 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.362 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.172 Order of pole (six term test) = -0.7722 TOP MAIN SOLVE Loop bytes used=76025512, alloc=4586680, time=2.64 x[1] = 2.33 y[1] (analytic) = 0 y[1] (numeric) = 1.2237116978000328309099536250568 absolute error = 1.2237116978000328309099536250568 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.368 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 = 3.18 Order of pole (six term test) = -0.7721 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0 y[1] (numeric) = 1.2289787877401856277507128439637 absolute error = 1.2289787877401856277507128439637 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.373 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 = 3.188 Order of pole (six term test) = -0.7721 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0 y[1] (numeric) = 1.2342464052728041274987575152018 absolute error = 1.2342464052728041274987575152018 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.379 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 = 3.196 Order of pole (six term test) = -0.772 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0 y[1] (numeric) = 1.2395145774905646963651929273813 absolute error = 1.2395145774905646963651929273813 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.384 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.204 Order of pole (six term test) = -0.7719 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0 y[1] (numeric) = 1.2447833314262009506492305560962 absolute error = 1.2447833314262009506492305560962 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.212 Order of pole (six term test) = -0.7719 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0 y[1] (numeric) = 1.2500526940532334371921624205255 absolute error = 1.2500526940532334371921624205255 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.395 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 = 3.22 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0 y[1] (numeric) = 1.2553226922866936861470288031799 absolute error = 1.2553226922866936861470288031799 relative error = -1 % Correct digits = -1 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 = 3.227 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0 y[1] (numeric) = 1.2605933529838427026132000496607 absolute error = 1.2605933529838427026132000496607 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.406 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 = 3.235 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0 y[1] (numeric) = 1.2658647029448839628251503938186 absolute error = 1.2658647029448839628251503938186 relative error = -1 % Correct digits = -1 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 = 3.243 Order of pole (six term test) = -0.7717 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 0 y[1] (numeric) = 1.2711367689136709797379368896878 absolute error = 1.2711367689136709797379368896878 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.417 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 = 3.251 Order of pole (six term test) = -0.7717 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0 y[1] (numeric) = 1.2764095775784095020180807750441 absolute error = 1.2764095775784095020180807750441 relative error = -1 % Correct digits = -1 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 = 3.259 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0 y[1] (numeric) = 1.2816831555723544096274576152062 absolute error = 1.2816831555723544096274576152062 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.428 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.267 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0 y[1] (numeric) = 1.286957529474501368379216428226 absolute error = 1.286957529474501368379216428226 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.434 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.275 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop bytes used=80026720, alloc=4586680, time=2.78 x[1] = 2.46 y[1] (analytic) = 0 y[1] (numeric) = 1.2922327258102733050484510031562 absolute error = 1.2922327258102733050484510031562 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.439 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.283 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 0 y[1] (numeric) = 1.2975087710522017638361273091522 absolute error = 1.2975087710522017638361273091522 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.445 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.291 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 0 y[1] (numeric) = 1.3027856916206032042124218701493 absolute error = 1.3027856916206032042124218701493 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.299 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 0 y[1] (numeric) = 1.308063513884250299404943872796 absolute error = 1.308063513884250299404943872796 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.456 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.307 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0 y[1] (numeric) = 1.3133422641610382940480991328072 absolute error = 1.3133422641610382940480991328072 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.461 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.315 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 0 y[1] (numeric) = 1.3186219687186464787719112549454 absolute error = 1.3186219687186464787719112549454 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.466 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.322 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0 y[1] (numeric) = 1.3239026537751948387817525297986 absolute error = 1.3239026537751948387817525297986 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.472 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.33 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 0 y[1] (numeric) = 1.3291843454998959327644661389189 absolute error = 1.3291843454998959327644661389189 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.477 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 = 3.338 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0 y[1] (numeric) = 1.3344670700137020577510975100955 absolute error = 1.3344670700137020577510975100955 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.483 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 = 3.346 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 0 y[1] (numeric) = 1.3397508533899477548717151203578 absolute error = 1.3397508533899477548717151203578 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.488 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.354 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 0 y[1] (numeric) = 1.3450357216549877102534120772681 absolute error = 1.3450357216549877102534120772681 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.494 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 = 3.362 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0 y[1] (numeric) = 1.3503217007888301046383651855277 absolute error = 1.3503217007888301046383651855277 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.499 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.37 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 0 y[1] (numeric) = 1.3556088167257654646346169958164 absolute error = 1.3556088167257654646346169958164 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.505 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 = 3.378 Order of pole (six term test) = -0.7712 bytes used=84028384, alloc=4586680, time=2.93 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0 y[1] (numeric) = 1.3608970953549910678578708400643 absolute error = 1.3608970953549910678578708400643 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.386 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 0 y[1] (numeric) = 1.3661865625212309535778845520185 absolute error = 1.3661865625212309535778845520185 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.516 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 = 3.394 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0 y[1] (numeric) = 1.3714772440253515898478540236734 absolute error = 1.3714772440253515898478540236734 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.521 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.402 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0 y[1] (numeric) = 1.3767691656249732474693345613512 absolute error = 1.3767691656249732474693345613512 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.527 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 = 3.41 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0 y[1] (numeric) = 1.3820623530350771305286007558486 absolute error = 1.3820623530350771305286007558486 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.532 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 = 3.418 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 0 y[1] (numeric) = 1.3873568319286083126327417545517 absolute error = 1.3873568319286083126327417545517 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.538 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.426 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 0 y[1] (numeric) = 1.3926526279370745273750787542421 absolute error = 1.3926526279370745273750787542421 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.543 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 = 3.434 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0 y[1] (numeric) = 1.3979497666511408609695283458993 absolute error = 1.3979497666511408609695283458993 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.549 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.442 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0 y[1] (numeric) = 1.4032482736212203944121748937602 absolute error = 1.4032482736212203944121748937602 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.554 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 = 3.45 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0 y[1] (numeric) = 1.4085481743580608419554159525845 absolute error = 1.4085481743580608419554159525845 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.458 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 0 y[1] (numeric) = 1.4138494943333272321154679724495 absolute error = 1.4138494943333272321154679724495 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.565 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.466 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0 y[1] (numeric) = 1.419152258980180676877628929097 absolute error = 1.419152258980180676877628929097 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.571 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.474 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 0 y[1] (numeric) = 1.4244564936938532742153562835348 absolute error = 1.4244564936938532742153562835348 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.576 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 = 3.482 Order of pole (six term test) = -0.7712 bytes used=88029624, alloc=4586680, time=3.06 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 0 y[1] (numeric) = 1.4297622238322191884988015134019 absolute error = 1.4297622238322191884988015134019 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.582 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.49 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0 y[1] (numeric) = 1.4350694747163619528358174788901 absolute error = 1.4350694747163619528358174788901 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.587 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.498 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 0 y[1] (numeric) = 1.4403782716311380368634955590827 absolute error = 1.4403782716311380368634955590827 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.593 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.506 Order of pole (six term test) = -0.7712 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 0 y[1] (numeric) = 1.445688639825736722990871606625 absolute error = 1.445688639825736722990871606625 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.598 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.514 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0 y[1] (numeric) = 1.4510006045142363335834413737432 absolute error = 1.4510006045142363335834413737432 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.604 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 = 3.522 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0 y[1] (numeric) = 1.4563141908761568510774274367357 absolute error = 1.4563141908761568510774274367357 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.609 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.53 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0 y[1] (numeric) = 1.4616294240570089725162232420815 absolute error = 1.4616294240570089725162232420815 relative error = -1 % Correct digits = -1 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 = 3.538 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0 y[1] (numeric) = 1.4669463291688396395129903011744 absolute error = 1.4669463291688396395129903011744 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.546 Order of pole (six term test) = -0.7713 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0 y[1] (numeric) = 1.47226493129077408416188844836 absolute error = 1.47226493129077408416188844836 relative error = -1 % Correct digits = -1 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 = 3.554 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 0 y[1] (numeric) = 1.4775852554695544309457651724337 absolute error = 1.4775852554695544309457651724337 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.631 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.562 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 0 y[1] (numeric) = 1.4829073267200748942202090659994 absolute error = 1.4829073267200748942202090659994 relative error = -1 % Correct digits = -1 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 = 3.57 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 0 y[1] (numeric) = 1.4882311700259136103925771078135 absolute error = 1.4882311700259136103925771078135 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.642 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 = 3.578 Order of pole (six term test) = -0.7714 TOP MAIN SOLVE Loop bytes used=92030352, alloc=4586680, time=3.20 x[1] = 2.84 y[1] (analytic) = 0 y[1] (numeric) = 1.4935568103398611434598304256552 absolute error = 1.4935568103398611434598304256552 relative error = -1 % Correct digits = -1 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 = 3.586 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0 y[1] (numeric) = 1.4988842725844457021206548956227 absolute error = 1.4988842725844457021206548956227 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.653 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 = 3.594 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 0 y[1] (numeric) = 1.5042135816524551062352997837857 absolute error = 1.5042135816524551062352997837857 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.658 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.602 Order of pole (six term test) = -0.7715 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0 y[1] (numeric) = 1.5095447624074555399707398082549 absolute error = 1.5095447624074555399707398082549 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.664 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 = 3.61 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 0 y[1] (numeric) = 1.5148778396843071285390554531405 absolute error = 1.5148778396843071285390554531405 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.669 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.618 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0 y[1] (numeric) = 1.5202128382896763750132368033135 absolute error = 1.5202128382896763750132368033135 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.675 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 = 3.626 Order of pole (six term test) = -0.7716 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0 y[1] (numeric) = 1.5255497830025454932868530022748 absolute error = 1.5255497830025454932868530022748 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.634 Order of pole (six term test) = -0.7717 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 0 y[1] (numeric) = 1.5308886985747186728320997521941 absolute error = 1.5308886985747186728320997521941 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.686 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 = 3.642 Order of pole (six term test) = -0.7717 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 0 y[1] (numeric) = 1.5362296097313253105045498052959 absolute error = 1.5362296097313253105045498052959 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.691 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.65 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0 y[1] (numeric) = 1.5415725411713202442423964795806 absolute error = 1.5415725411713202442423964795806 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.697 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.658 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 0 y[1] (numeric) = 1.5469175175679810231130097885443 absolute error = 1.5469175175679810231130097885443 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.702 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 = 3.666 Order of pole (six term test) = -0.7719 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0 y[1] (numeric) = 1.5522645635694022477701322712484 absolute error = 1.5522645635694022477701322712484 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.708 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.674 Order of pole (six term test) = -0.7719 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0 y[1] (numeric) = 1.5576137037989870150009420307339 absolute error = 1.5576137037989870150009420307339 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.713 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 = 3.682 Order of pole (six term test) = -0.772 TOP MAIN SOLVE Loop bytes used=96032132, alloc=4652204, time=3.35 x[1] = 2.97 y[1] (analytic) = 0 y[1] (numeric) = 1.5629649628559354996634203085924 absolute error = 1.5629649628559354996634203085924 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.719 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.69 Order of pole (six term test) = -0.772 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0 y[1] (numeric) = 1.5683183653157307069408980740642 absolute error = 1.5683183653157307069408980740642 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.724 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 = 3.698 Order of pole (six term test) = -0.7721 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 0 y[1] (numeric) = 1.5736739357306214274722399509888 absolute error = 1.5736739357306214274722399509888 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.707 Order of pole (six term test) = -0.7721 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 0 y[1] (numeric) = 1.5790316986301024275527751123346 absolute error = 1.5790316986301024275527751123346 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.735 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 = 3.715 Order of pole (six term test) = -0.7722 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 0 y[1] (numeric) = 1.5843916785213919062427256832332 absolute error = 1.5843916785213919062427256832332 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.741 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.723 Order of pole (six term test) = -0.7722 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 0 y[1] (numeric) = 1.5897538998899062508664372025824 absolute error = 1.5897538998899062508664372025824 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.746 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.731 Order of pole (six term test) = -0.7723 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 0 y[1] (numeric) = 1.5951183871997321220371076173417 absolute error = 1.5951183871997321220371076173417 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.752 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 = 3.739 Order of pole (six term test) = -0.7724 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 0 y[1] (numeric) = 1.6004851648940958989978672380214 absolute error = 1.6004851648940958989978672380214 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.757 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.747 Order of pole (six term test) = -0.7724 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 0 y[1] (numeric) = 1.605854257395830515730909457535 absolute error = 1.605854257395830515730909457535 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.762 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.755 Order of pole (six term test) = -0.7725 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 0 y[1] (numeric) = 1.6112256891078397179518394667203 absolute error = 1.6112256891078397179518394667203 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.768 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.763 Order of pole (six term test) = -0.7725 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 0 y[1] (numeric) = 1.6165994844135597707764255520059 absolute error = 1.6165994844135597707764255520059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.773 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.771 Order of pole (six term test) = -0.7726 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 0 y[1] (numeric) = 1.6219756676774186465214358995171 absolute error = 1.6219756676774186465214358995171 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.779 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.779 Order of pole (six term test) = -0.7727 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 0 y[1] (numeric) = 1.6273542632452927217801554002093 absolute error = 1.6273542632452927217801554002093 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.784 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.787 Order of pole (six term test) = -0.7727 TOP MAIN SOLVE Loop bytes used=100033220, alloc=4652204, time=3.49 x[1] = 3.1 y[1] (analytic) = 0 y[1] (numeric) = 1.6327352954449610125964351540452 absolute error = 1.6327352954449610125964351540452 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.796 Order of pole (six term test) = -0.7728 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 0 y[1] (numeric) = 1.638118788586556976248666744412 absolute error = 1.638118788586556976248666744412 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.795 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.804 Order of pole (six term test) = -0.7729 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 0 y[1] (numeric) = 1.643504766963017907846829547008 absolute error = 1.643504766963017907846829547008 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.801 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 = 3.812 Order of pole (six term test) = -0.773 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 0 y[1] (numeric) = 1.6488932548505319596416690929366 absolute error = 1.6488932548505319596416690929366 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.806 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.82 Order of pole (six term test) = -0.773 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 0 y[1] (numeric) = 1.6542842765089828106450656382773 absolute error = 1.6542842765089828106450656382773 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.812 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 = 3.828 Order of pole (six term test) = -0.7731 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 0 y[1] (numeric) = 1.6596778561823920138646834683298 absolute error = 1.6596778561823920138646834683298 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.817 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 = 3.836 Order of pole (six term test) = -0.7732 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 0 y[1] (numeric) = 1.6650740180993590481639929824931 absolute error = 1.6650740180993590481639929824931 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.823 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 = 3.844 Order of pole (six term test) = -0.7733 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0 y[1] (numeric) = 1.6704727864734991014706701765797 absolute error = 1.6704727864734991014706701765797 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.828 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 = 3.852 Order of pole (six term test) = -0.7734 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0 y[1] (numeric) = 1.6758741855038786117721436683556 absolute error = 1.6758741855038786117721436683556 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.834 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 = 3.861 Order of pole (six term test) = -0.7734 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 0 y[1] (numeric) = 1.6812782393754485920566207796734 absolute error = 1.6812782393754485920566207796734 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.839 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 = 3.869 Order of pole (six term test) = -0.7735 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0 y[1] (numeric) = 1.6866849722594757650812252323254 absolute error = 1.6866849722594757650812252323254 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.845 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.877 Order of pole (six term test) = -0.7736 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 0 y[1] (numeric) = 1.6920944083139715335758645117251 absolute error = 1.6920944083139715335758645117251 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.885 Order of pole (six term test) = -0.7737 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0 y[1] (numeric) = 1.6975065716841188112220606017432 absolute error = 1.6975065716841188112220606017432 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.856 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.893 Order of pole (six term test) = -0.7738 TOP MAIN SOLVE Loop bytes used=104034392, alloc=4652204, time=3.63 x[1] = 3.23 y[1] (analytic) = 0 y[1] (numeric) = 1.7029214865026967394801701994636 absolute error = 1.7029214865026967394801701994636 relative error = -1 % Correct digits = -1 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 = 3.901 Order of pole (six term test) = -0.7739 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 0 y[1] (numeric) = 1.7083391768905033150761371724872 absolute error = 1.7083391768905033150761371724872 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.867 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.91 Order of pole (six term test) = -0.774 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0 y[1] (numeric) = 1.713759666956775952700109287779 absolute error = 1.713759666956775952700109287779 relative error = -1 % Correct digits = -1 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 = 3.918 Order of pole (six term test) = -0.7741 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0 y[1] (numeric) = 1.7191829807996100072138623398372 absolute error = 1.7191829807996100072138623398372 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.878 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.926 Order of pole (six term test) = -0.7742 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0 y[1] (numeric) = 1.7246091425063752794119577971792 absolute error = 1.7246091425063752794119577971792 relative error = -1 % Correct digits = -1 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 = 3.934 Order of pole (six term test) = -0.7743 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 0 y[1] (numeric) = 1.7300381761541305291328658545424 absolute error = 1.7300381761541305291328658545424 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.889 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.942 Order of pole (six term test) = -0.7744 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0 y[1] (numeric) = 1.7354701058100360192708660181627 absolute error = 1.7354701058100360192708660181627 relative error = -1 % Correct digits = -1 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 = 3.95 Order of pole (six term test) = -0.7745 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 0 y[1] (numeric) = 1.7409049555317641139973445522612 absolute error = 1.7409049555317641139973445522612 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.9 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 = 3.959 Order of pole (six term test) = -0.7746 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0 y[1] (numeric) = 1.74634274936790795426109554604 absolute error = 1.74634274936790795426109554604 relative error = -1 % Correct digits = -1 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 = 3.967 Order of pole (six term test) = -0.7747 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0 y[1] (numeric) = 1.7517835113583882334013540578509 absolute error = 1.7517835113583882334013540578509 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.975 Order of pole (six term test) = -0.7748 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 0 y[1] (numeric) = 1.7572272655348580954745005447906 absolute error = 1.7572272655348580954745005447906 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.916 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.983 Order of pole (six term test) = -0.7749 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0 y[1] (numeric) = 1.7626740359211061786656311184863 absolute error = 1.7626740359211061786656311184863 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.921 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.991 Order of pole (six term test) = -0.775 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 0 y[1] (numeric) = 1.768123846533457825929444333208 absolute error = 1.768123846533457825929444333208 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.927 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -0.7751 TOP MAIN SOLVE Loop bytes used=108035464, alloc=4652204, time=3.77 x[1] = 3.36 y[1] (analytic) = 0 y[1] (numeric) = 1.7735767213811744847811091748165 absolute error = 1.7735767213811744847811091748165 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.932 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.008 Order of pole (six term test) = -0.7752 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0 y[1] (numeric) = 1.7790326844668513179369083419016 absolute error = 1.7790326844668513179369083419016 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.938 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.016 Order of pole (six term test) = -0.7753 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 0 y[1] (numeric) = 1.7844917597868130462864541440238 absolute error = 1.7844917597868130462864541440238 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.943 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.024 Order of pole (six term test) = -0.7754 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 0 y[1] (numeric) = 1.7899539713315080454631104109204 absolute error = 1.7899539713315080454631104109204 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.949 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.032 Order of pole (six term test) = -0.7755 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0 y[1] (numeric) = 1.7954193430859007170668823978887 absolute error = 1.7954193430859007170668823978887 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.954 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.041 Order of pole (six term test) = -0.7756 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 0 y[1] (numeric) = 1.8008878990298621553844181238392 absolute error = 1.8008878990298621553844181238392 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.96 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 = 4.049 Order of pole (six term test) = -0.7758 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 0 y[1] (numeric) = 1.8063596631385591302438598661135 absolute error = 1.8063596631385591302438598661135 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.965 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 = 4.057 Order of pole (six term test) = -0.7759 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0 y[1] (numeric) = 1.811834659382841406438055263984 absolute error = 1.811834659382841406438055263984 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.971 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 = 4.065 Order of pole (six term test) = -0.776 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0 y[1] (numeric) = 1.8173129117296274199480458710194 absolute error = 1.8173129117296274199480458710194 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.976 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 = 4.074 Order of pole (six term test) = -0.7761 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0 y[1] (numeric) = 1.822794444142288330999759870822 absolute error = 1.822794444142288330999759870822 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.982 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 = 4.082 Order of pole (six term test) = -0.7762 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 0 y[1] (numeric) = 1.828279280581030473790408451284 absolute error = 1.828279280581030473790408451284 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.987 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 = 4.09 Order of pole (six term test) = -0.7764 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 0 y[1] (numeric) = 1.8337674450032762225271860238684 absolute error = 1.8337674450032762225271860238684 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.993 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 = 4.098 Order of pole (six term test) = -0.7765 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0 y[1] (numeric) = 1.8392589613640432932294676547055 absolute error = 1.8392589613640432932294676547055 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.998 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 = 4.107 Order of pole (six term test) = -0.7766 TOP MAIN SOLVE Loop bytes used=112037040, alloc=4652204, time=3.92 x[1] = 3.49 y[1] (analytic) = 0 y[1] (numeric) = 1.8447538536163225005567478854165 absolute error = 1.8447538536163225005567478854165 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.004 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 = 4.115 Order of pole (six term test) = -0.7767 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 0 y[1] (numeric) = 1.8502521457114539887380392592184 absolute error = 1.8502521457114539887380392592184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.009 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 = 4.123 Order of pole (six term test) = -0.7769 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 0 y[1] (numeric) = 1.8557538615995019554943125717623 absolute error = 1.8557538615995019554943125717623 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.015 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.131 Order of pole (six term test) = -0.777 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 0 y[1] (numeric) = 1.8612590252296278876637809105554 absolute error = 1.8612590252296278876637809105554 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.14 Order of pole (six term test) = -0.7771 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0 y[1] (numeric) = 1.8667676605504623270603732311105 absolute error = 1.8667676605504623270603732311105 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.026 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.148 Order of pole (six term test) = -0.7772 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0 y[1] (numeric) = 1.8722797915104751849185783575257 absolute error = 1.8722797915104751849185783575257 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.031 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.156 Order of pole (six term test) = -0.7774 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0 y[1] (numeric) = 1.8777954420583446231029352123761 absolute error = 1.8777954420583446231029352123761 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.037 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.164 Order of pole (six term test) = -0.7775 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 0 y[1] (numeric) = 1.8833146361433245200877685960922 absolute error = 1.8833146361433245200877685960922 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.042 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.173 Order of pole (six term test) = -0.7776 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 0 y[1] (numeric) = 1.8888373977156105395422912594009 absolute error = 1.8888373977156105395422912594009 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.048 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.181 Order of pole (six term test) = -0.7778 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0 y[1] (numeric) = 1.8943637507267048191878821349114 absolute error = 1.8943637507267048191878821349114 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.053 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.189 Order of pole (six term test) = -0.7779 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0 y[1] (numeric) = 1.8998937191297792974281776791945 absolute error = 1.8998937191297792974281776791945 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.059 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 = 4.198 Order of pole (six term test) = -0.7781 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 0 y[1] (numeric) = 1.9054273268800376950885490529026 absolute error = 1.9054273268800376950885490529026 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.064 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.206 Order of pole (six term test) = -0.7782 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0 y[1] (numeric) = 1.9109645979350761694395535182514 absolute error = 1.9109645979350761694395535182514 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.069 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.214 Order of pole (six term test) = -0.7783 TOP MAIN SOLVE Loop bytes used=116037996, alloc=4652204, time=4.06 x[1] = 3.62 y[1] (analytic) = 0 y[1] (numeric) = 1.9165055562552426575190155937973 absolute error = 1.9165055562552426575190155937973 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.075 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.222 Order of pole (six term test) = -0.7785 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 0 y[1] (numeric) = 1.9220502258039949256094842500809 absolute error = 1.9220502258039949256094842500809 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.231 Order of pole (six term test) = -0.7786 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0 y[1] (numeric) = 1.9275986305482573415718992638653 absolute error = 1.9275986305482573415718992638653 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.086 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = -0.7788 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 0 y[1] (numeric) = 1.9331507944587763865823557068127 absolute error = 1.9331507944587763865823557068127 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.091 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.247 Order of pole (six term test) = -0.7789 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0 y[1] (numeric) = 1.9387067415104749226668537785598 absolute error = 1.9387067415104749226668537785598 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.097 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.256 Order of pole (six term test) = -0.7791 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0 y[1] (numeric) = 1.944266495682805232278835567801 absolute error = 1.944266495682805232278835567801 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.102 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.264 Order of pole (six term test) = -0.7792 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 0 y[1] (numeric) = 1.9498300809601008460161150061682 absolute error = 1.9498300809601008460161150061682 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.108 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.272 Order of pole (six term test) = -0.7794 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0 y[1] (numeric) = 1.9553975213319271744274768339795 absolute error = 1.9553975213319271744274768339795 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.113 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 = 4.281 Order of pole (six term test) = -0.7795 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 0 y[1] (numeric) = 1.960968840793430959714729780727 absolute error = 1.960968840793430959714729780727 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.119 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.289 Order of pole (six term test) = -0.7797 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0 y[1] (numeric) = 1.9665440633456885629933237170961 absolute error = 1.9665440633456885629933237170961 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.124 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 = 4.297 Order of pole (six term test) = -0.7798 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0 y[1] (numeric) = 1.9721232129960531026337559776601 absolute error = 1.9721232129960531026337559776601 relative error = -1 % Correct digits = -1 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 = 4.306 Order of pole (six term test) = -0.78 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 0 y[1] (numeric) = 1.9777063137585004590668744738098 absolute error = 1.9777063137585004590668744738098 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.135 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 = 4.314 Order of pole (six term test) = -0.7801 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 0 y[1] (numeric) = 1.9832933896539741612988110696235 absolute error = 1.9832933896539741612988110696235 relative error = -1 % Correct digits = -1 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 = 4.322 Order of pole (six term test) = -0.7803 TOP MAIN SOLVE Loop bytes used=120038912, alloc=4652204, time=4.20 x[1] = 3.75 y[1] (analytic) = 0 y[1] (numeric) = 1.9888844647107291702456247928593 absolute error = 1.9888844647107291702456247928593 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.146 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 = 4.331 Order of pole (six term test) = -0.7805 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0 y[1] (numeric) = 1.9944795629646745738637779655035 absolute error = 1.9944795629646745738637779655035 relative error = -1 % Correct digits = -1 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 = 4.339 Order of pole (six term test) = -0.7806 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 0 y[1] (numeric) = 2.0000787084597152089202867767593 absolute error = 2.0000787084597152089202867767593 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.157 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 = 4.347 Order of pole (six term test) = -0.7808 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0 y[1] (numeric) = 2.005681925248092224115759040544 absolute error = 2.005681925248092224115759040544 relative error = -1 % Correct digits = -1 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 = 4.356 Order of pole (six term test) = -0.7809 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 0 y[1] (numeric) = 2.0112892373907225991445340694799 absolute error = 2.0112892373907225991445340694799 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.168 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.364 Order of pole (six term test) = -0.7811 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0 y[1] (numeric) = 2.0169006689575376341487512778172 absolute error = 2.0169006689575376341487512778172 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.174 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.373 Order of pole (six term test) = -0.7813 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0 y[1] (numeric) = 2.0225162440278204238973741408828 absolute error = 2.0225162440278204238973741408828 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.179 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.381 Order of pole (six term test) = -0.7814 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0 y[1] (numeric) = 2.0281359866905423308969636515959 absolute error = 2.0281359866905423308969636515959 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.185 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.389 Order of pole (six term test) = -0.7816 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 0 y[1] (numeric) = 2.0337599210446984715183099020762 absolute error = 2.0337599210446984715183099020762 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.398 Order of pole (six term test) = -0.7818 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 0 y[1] (numeric) = 2.0393880711996422291018716655689 absolute error = 2.0393880711996422291018716655689 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.196 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.406 Order of pole (six term test) = -0.7819 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 0 y[1] (numeric) = 2.0450204612754188078853219493551 absolute error = 2.0450204612754188078853219493551 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.201 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.414 Order of pole (six term test) = -0.7821 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 0 y[1] (numeric) = 2.0506571154030978414783328198407 absolute error = 2.0506571154030978414783328198407 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.207 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.423 Order of pole (six term test) = -0.7823 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0 y[1] (numeric) = 2.0562980577251050694930360468837 absolute error = 2.0562980577251050694930360468837 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.212 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.431 Order of pole (six term test) = -0.7825 TOP MAIN SOLVE Loop bytes used=124040804, alloc=4652204, time=4.34 x[1] = 3.88 y[1] (analytic) = 0 y[1] (numeric) = 2.0619433123955530958233482444464 absolute error = 2.0619433123955530958233482444464 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.217 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.44 Order of pole (six term test) = -0.7826 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0 y[1] (numeric) = 2.0675929035805712419525314514981 absolute error = 2.0675929035805712419525314514981 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.223 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.448 Order of pole (six term test) = -0.7828 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 0 y[1] (numeric) = 2.0732468554586345085559540325673 absolute error = 2.0732468554586345085559540325673 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.228 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.456 Order of pole (six term test) = -0.783 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0 y[1] (numeric) = 2.0789051922208916585550041878693 absolute error = 2.0789051922208916585550041878693 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.234 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 = 4.465 Order of pole (six term test) = -0.7832 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 0 y[1] (numeric) = 2.0845679380714924346684713250312 absolute error = 2.0845679380714924346684713250312 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.239 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.473 Order of pole (six term test) = -0.7833 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0 y[1] (numeric) = 2.0902351172279139243994314003229 absolute error = 2.0902351172279139243994314003229 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.245 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 = 4.482 Order of pole (six term test) = -0.7835 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0 y[1] (numeric) = 2.0959067539212860852887336905532 absolute error = 2.0959067539212860852887336905532 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.49 Order of pole (six term test) = -0.7837 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 0 y[1] (numeric) = 2.1015828723967164431605711680871 absolute error = 2.1015828723967164431605711680871 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.256 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 = 4.498 Order of pole (six term test) = -0.7839 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 0 y[1] (numeric) = 2.1072634969136139759813078344069 absolute error = 2.1072634969136139759813078344069 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.261 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.507 Order of pole (six term test) = -0.7841 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 0 y[1] (numeric) = 2.1129486517460121958497173847148 absolute error = 2.1129486517460121958497173847148 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.267 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 = 4.515 Order of pole (six term test) = -0.7842 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0 y[1] (numeric) = 2.1186383611828914415350420345052 absolute error = 2.1186383611828914415350420345052 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.272 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 = 4.524 Order of pole (six term test) = -0.7844 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0 y[1] (numeric) = 2.1243326495285003938787920869072 absolute error = 2.1243326495285003938787920869072 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.278 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.532 Order of pole (six term test) = -0.7846 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0 y[1] (numeric) = 2.1300315411026768262769599419524 absolute error = 2.1300315411026768262769599419524 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.283 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 = 4.541 Order of pole (six term test) = -0.7848 TOP MAIN SOLVE Loop bytes used=128043760, alloc=4652204, time=4.49 x[1] = 4.01 y[1] (analytic) = 0 y[1] (numeric) = 2.1357350602411676023613010639382 absolute error = 2.1357350602411676023613010639382 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.289 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.549 Order of pole (six term test) = -0.785 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 0 y[1] (numeric) = 2.141443231295947932901523478301 absolute error = 2.141443231295947932901523478301 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.294 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 = 4.557 Order of pole (six term test) = -0.7852 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0 y[1] (numeric) = 2.1471560786355399038546114381495 absolute error = 2.1471560786355399038546114381495 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.566 Order of pole (six term test) = -0.7854 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 0 y[1] (numeric) = 2.1528736266453302873930729781997 absolute error = 2.1528736266453302873930729781997 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.305 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 = 4.574 Order of pole (six term test) = -0.7856 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0 y[1] (numeric) = 2.1585958997278876476506303741765 absolute error = 2.1585958997278876476506303741765 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.311 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.583 Order of pole (six term test) = -0.7857 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 0 y[1] (numeric) = 2.1643229223032787528317524777308 absolute error = 2.1643229223032787528317524777308 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.316 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 = 4.591 Order of pole (six term test) = -0.7859 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 0 y[1] (numeric) = 2.170054718809384305240444141098 absolute error = 2.170054718809384305240444141098 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.322 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.6 Order of pole (six term test) = -0.7861 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0 y[1] (numeric) = 2.1757913137022140006938463308635 absolute error = 2.1757913137022140006938463308635 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.327 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.608 Order of pole (six term test) = -0.7863 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0 y[1] (numeric) = 2.1815327314562209286974471100031 absolute error = 2.1815327314562209286974471100031 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.333 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.617 Order of pole (six term test) = -0.7865 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0 y[1] (numeric) = 2.1872789965646153246710446972056 absolute error = 2.1872789965646153246710446972056 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.338 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.625 Order of pole (six term test) = -0.7867 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 0 y[1] (numeric) = 2.1930301335396776854280257462127 absolute error = 2.1930301335396776854280257462127 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.344 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.634 Order of pole (six term test) = -0.7869 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 0 y[1] (numeric) = 2.1987861669130712590250114747197 absolute error = 2.1987861669130712590250114747197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.349 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.642 Order of pole (six term test) = -0.7871 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0 y[1] (numeric) = 2.2045471212361539200144681537173 absolute error = 2.2045471212361539200144681537173 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.355 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.651 Order of pole (six term test) = -0.7873 TOP MAIN SOLVE Loop bytes used=132044632, alloc=4652204, time=4.63 x[1] = 4.14 y[1] (analytic) = 0 y[1] (numeric) = 2.2103130210802894410494637746809 absolute error = 2.2103130210802894410494637746809 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.659 Order of pole (six term test) = -0.7875 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 0 y[1] (numeric) = 2.2160838910371581717073666606466 absolute error = 2.2160838910371581717073666606466 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.366 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.668 Order of pole (six term test) = -0.7877 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0 y[1] (numeric) = 2.2218597557190671353179117781731 absolute error = 2.2218597557190671353179117781731 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.371 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.676 Order of pole (six term test) = -0.7879 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0 y[1] (numeric) = 2.2276406397592595545006941211425 absolute error = 2.2276406397592595545006941211425 relative error = -1 % Correct digits = -1 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 = 4.685 Order of pole (six term test) = -0.7881 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 0 y[1] (numeric) = 2.2334265678122238160377735325806 absolute error = 2.2334265678122238160377735325806 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.382 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 = 4.693 Order of pole (six term test) = -0.7883 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0 y[1] (numeric) = 2.2392175645540018856286796402855 absolute error = 2.2392175645540018856286796402855 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.387 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.702 Order of pole (six term test) = -0.7885 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0 y[1] (numeric) = 2.2450136546824971829976773112656 absolute error = 2.2450136546824971829976773112656 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.393 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 = 4.71 Order of pole (six term test) = -0.7887 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 0 y[1] (numeric) = 2.2508148629177819277466804534386 absolute error = 2.2508148629177819277466804534386 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.398 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.718 Order of pole (six term test) = -0.7889 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0 y[1] (numeric) = 2.256621214002403966271673552157 absolute error = 2.256621214002403966271673552157 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.404 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 = 4.727 Order of pole (six term test) = -0.7891 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 0 y[1] (numeric) = 2.2624327327016930899859046295209 absolute error = 2.2624327327016930899859046295209 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.409 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.736 Order of pole (six term test) = -0.7893 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 0 y[1] (numeric) = 2.2682494438040668550194391233759 absolute error = 2.2682494438040668550194391233759 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.415 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 = 4.744 Order of pole (six term test) = -0.7895 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0 y[1] (numeric) = 2.2740713721213359134919004267843 absolute error = 2.2740713721213359134919004267843 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.753 Order of pole (six term test) = -0.7897 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0 y[1] (numeric) = 2.2798985424890088663833585906805 absolute error = 2.2798985424890088663833585906805 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.426 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 = 4.761 Order of pole (six term test) = -0.7899 TOP MAIN SOLVE Loop bytes used=136045664, alloc=4652204, time=4.77 x[1] = 4.27 y[1] (analytic) = 0 y[1] (numeric) = 2.2857309797665966479573532097385 absolute error = 2.2857309797665966479573532097385 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.431 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 = 4.77 Order of pole (six term test) = -0.7901 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0 y[1] (numeric) = 2.2915687088379164516199391734153 absolute error = 2.2915687088379164516199391734153 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.437 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.778 Order of pole (six term test) = -0.7904 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 0 y[1] (numeric) = 2.297411754611395207029414309487 absolute error = 2.297411754611395207029414309487 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.442 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 = 4.787 Order of pole (six term test) = -0.7906 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 0 y[1] (numeric) = 2.303260142020372618203015662185 absolute error = 2.303260142020372618203015662185 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.448 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.795 Order of pole (six term test) = -0.7908 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 0 y[1] (numeric) = 2.3091138960234037722993460623127 absolute error = 2.3091138960234037722993460623127 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.453 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 = 4.804 Order of pole (six term test) = -0.791 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0 y[1] (numeric) = 2.314973041604561328688604736265 absolute error = 2.314973041604561328688604736265 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.459 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.812 Order of pole (six term test) = -0.7912 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0 y[1] (numeric) = 2.3208376037737372978568350790809 absolute error = 2.3208376037737372978568350790809 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.464 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 = 4.821 Order of pole (six term test) = -0.7914 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 0 y[1] (numeric) = 2.3267076075669444196253596363688 absolute error = 2.3267076075669444196253596363688 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.829 Order of pole (six term test) = -0.7916 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0 y[1] (numeric) = 2.3325830780466171501023371903143 absolute error = 2.3325830780466171501023371903143 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.475 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 = 4.838 Order of pole (six term test) = -0.7918 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0 y[1] (numeric) = 2.3384640403019122667199401494477 absolute error = 2.3384640403019122667199401494477 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.481 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.846 Order of pole (six term test) = -0.792 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0 y[1] (numeric) = 2.3443505194490091006480028560524 absolute error = 2.3443505194490091006480028560524 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.486 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.855 Order of pole (six term test) = -0.7923 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 0 y[1] (numeric) = 2.3502425406314094058131237349049 absolute error = 2.3502425406314094058131237349049 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.492 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 = 4.863 Order of pole (six term test) = -0.7925 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 0 y[1] (numeric) = 2.3561401290202368736911073265529 absolute error = 2.3561401290202368736911073265529 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.497 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.872 Order of pole (six term test) = -0.7927 TOP MAIN SOLVE Loop bytes used=140046600, alloc=4652204, time=4.91 x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 2.3620433098145363029802972179747 absolute error = 2.3620433098145363029802972179747 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.503 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 = 4.88 Order of pole (six term test) = -0.7929 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 0 y[1] (numeric) = 2.3679521082415724332037688680277 absolute error = 2.3679521082415724332037688680277 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.508 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.889 Order of pole (six term test) = -0.7931 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0 y[1] (numeric) = 2.3738665495571284512295136119221 absolute error = 2.3738665495571284512295136119221 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.514 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 = 4.898 Order of pole (six term test) = -0.7933 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 0 y[1] (numeric) = 2.3797866590458041796396431260614 absolute error = 2.3797866590458041796396431260614 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.519 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.906 Order of pole (six term test) = -0.7935 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0 y[1] (numeric) = 2.3857124620213139558222688688589 absolute error = 2.3857124620213139558222688688589 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.525 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 = 4.915 Order of pole (six term test) = -0.7938 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 0 y[1] (numeric) = 2.391643983826784210603055128536 absolute error = 2.391643983826784210603055128536 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.53 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 = 4.923 Order of pole (six term test) = -0.794 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0 y[1] (numeric) = 2.3975812498350507551774990647405 absolute error = 2.3975812498350507551774990647405 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.535 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 = 4.932 Order of pole (six term test) = -0.7942 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 0 y[1] (numeric) = 2.4035242854489557850497483999967 absolute error = 2.4035242854489557850497483999967 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.541 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 = 4.94 Order of pole (six term test) = -0.7944 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 0 y[1] (numeric) = 2.409473116101644609629219184346 absolute error = 2.409473116101644609629219184346 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.546 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 = 4.949 Order of pole (six term test) = -0.7946 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0 y[1] (numeric) = 2.4154277672568621160824144171226 absolute error = 2.4154277672568621160824144171226 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.552 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 = 4.957 Order of pole (six term test) = -0.7949 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 2.4213882644092489759841614673148 absolute error = 2.4213882644092489759841614673148 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.557 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.966 Order of pole (six term test) = -0.7951 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 0 y[1] (numeric) = 2.4273546330846376032599744990584 absolute error = 2.4273546330846376032599744990584 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.563 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 = 4.974 Order of pole (six term test) = -0.7953 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 0 y[1] (numeric) = 2.433326898840347871859399897573 absolute error = 2.433326898840347871859399897573 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.568 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.983 Order of pole (six term test) = -0.7955 TOP MAIN SOLVE Loop bytes used=144048116, alloc=4652204, time=5.06 x[1] = 4.53 y[1] (analytic) = 0 y[1] (numeric) = 2.4393050872654826015490105232055 absolute error = 2.4393050872654826015490105232055 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.574 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 = 4.992 Order of pole (six term test) = -0.7957 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0 y[1] (numeric) = 2.4452892239812228201631711194298 absolute error = 2.4452892239812228201631711194298 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.579 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5 Order of pole (six term test) = -0.7959 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 0 y[1] (numeric) = 2.4512793346411228106007950876955 absolute error = 2.4512793346411228106007950876955 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.585 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.009 Order of pole (six term test) = -0.7962 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 0 y[1] (numeric) = 2.4572754449314049508070449402843 absolute error = 2.4572754449314049508070449402843 relative error = -1 % Correct digits = -1 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 = 5.017 Order of pole (six term test) = -0.7964 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 0 y[1] (numeric) = 2.4632775805712543549302879720197 absolute error = 2.4632775805712543549302879720197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.596 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.026 Order of pole (six term test) = -0.7966 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 0 y[1] (numeric) = 2.4692857673131133237965980694204 absolute error = 2.4692857673131133237965980694204 relative error = -1 % Correct digits = -1 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 = 5.034 Order of pole (six term test) = -0.7968 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 0 y[1] (numeric) = 2.4753000309429756127966872133145 absolute error = 2.4753000309429756127966872133145 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.607 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.043 Order of pole (six term test) = -0.797 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 2.4813203972806805252333493332894 absolute error = 2.4813203972806805252333493332894 relative error = -1 % Correct digits = -1 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 = 5.051 Order of pole (six term test) = -0.7973 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 0 y[1] (numeric) = 2.4873468921802068391312980371332 absolute error = 2.4873468921802068391312980371332 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.618 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.06 Order of pole (six term test) = -0.7975 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 0 y[1] (numeric) = 2.4933795415299665754656717540168 absolute error = 2.4933795415299665754656717540168 relative error = -1 % Correct digits = -1 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 = 5.069 Order of pole (six term test) = -0.7977 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 0 y[1] (numeric) = 2.4994183712530986157204584745346 absolute error = 2.4994183712530986157204584745346 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.629 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.077 Order of pole (six term test) = -0.7979 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 0 y[1] (numeric) = 2.505463407307762176643651110113 absolute error = 2.505463407307762176643651110113 relative error = -1 % Correct digits = -1 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 = 5.086 Order of pole (six term test) = -0.7981 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 0 y[1] (numeric) = 2.5115146756874301500220771819257 absolute error = 2.5115146756874301500220771819257 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.094 Order of pole (six term test) = -0.7984 TOP MAIN SOLVE Loop bytes used=148048884, alloc=4652204, time=5.20 x[1] = 4.66 y[1] (analytic) = 0 y[1] (numeric) = 2.5175722024211823152555468242922 absolute error = 2.5175722024211823152555468242922 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.645 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.103 Order of pole (six term test) = -0.7986 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 0 y[1] (numeric) = 2.5236360135739984324672247730179 absolute error = 2.5236360135739984324672247730179 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.651 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 = 5.111 Order of pole (six term test) = -0.7988 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 0 y[1] (numeric) = 2.5297061352470512238449490119793 absolute error = 2.5297061352470512238449490119793 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.656 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.12 Order of pole (six term test) = -0.799 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 0 y[1] (numeric) = 2.5357825935779992508665850602372 absolute error = 2.5357825935779992508665850602372 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.662 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 = 5.128 Order of pole (six term test) = -0.7992 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 0 y[1] (numeric) = 2.5418654147412796950214145667435 absolute error = 2.5418654147412796950214145667435 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.667 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.137 Order of pole (six term test) = -0.7995 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 0 y[1] (numeric) = 2.547954624948401049599004089665 absolute error = 2.547954624948401049599004089665 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.673 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 = 5.146 Order of pole (six term test) = -0.7997 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 0 y[1] (numeric) = 2.5540502504482357300769789004432 absolute error = 2.5540502504482357300769789004432 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.678 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.154 Order of pole (six term test) = -0.7999 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 0 y[1] (numeric) = 2.5601523175273126105996316743421 absolute error = 2.5601523175273126105996316743421 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.684 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 = 5.163 Order of pole (six term test) = -0.8001 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 0 y[1] (numeric) = 2.5662608525101094940003213911507 absolute error = 2.5662608525101094940003213911507 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.689 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 = 5.171 Order of pole (six term test) = -0.8003 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 0 y[1] (numeric) = 2.5723758817593455227821581288977 absolute error = 2.5723758817593455227821581288977 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.694 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.18 Order of pole (six term test) = -0.8005 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 0 y[1] (numeric) = 2.5784974316762735384335192210662 absolute error = 2.5784974316762735384335192210662 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.7 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 = 5.188 Order of pole (six term test) = -0.8008 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 0 y[1] (numeric) = 2.584625528700972396417496068156 absolute error = 2.584625528700972396417496068156 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.705 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.197 Order of pole (six term test) = -0.801 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 0 y[1] (numeric) = 2.590760199312639244137423423891 absolute error = 2.590760199312639244137423423891 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.711 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 = 5.205 Order of pole (six term test) = -0.8012 TOP MAIN SOLVE Loop bytes used=152051872, alloc=4652204, time=5.34 x[1] = 4.79 y[1] (analytic) = 0 y[1] (numeric) = 2.5969014700298817691441889623305 absolute error = 2.5969014700298817691441889623305 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.716 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 = 5.214 Order of pole (six term test) = -0.8014 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 0 y[1] (numeric) = 2.6030493674110104248150551920822 absolute error = 2.6030493674110104248150551920822 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.722 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 = 5.222 Order of pole (six term test) = -0.8016 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 0 y[1] (numeric) = 2.6092039180543306406982432042529 absolute error = 2.6092039180543306406982432042529 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.727 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 = 5.231 Order of pole (six term test) = -0.8018 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 0 y[1] (numeric) = 2.615365148598435024682523276315 absolute error = 2.615365148598435024682523276315 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.733 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 = 5.24 Order of pole (six term test) = -0.802 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 0 y[1] (numeric) = 2.6215330857224955641165260264368 absolute error = 2.6215330857224955641165260264368 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.738 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 = 5.248 Order of pole (six term test) = -0.8022 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 0 y[1] (numeric) = 2.627707756146555832968424709916 absolute error = 2.627707756146555832968424709916 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.744 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.257 Order of pole (six term test) = -0.8025 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 0 y[1] (numeric) = 2.6338891866318232120830395243148 absolute error = 2.6338891866318232120830395243148 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.749 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 = 5.265 Order of pole (six term test) = -0.8027 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 0 y[1] (numeric) = 2.640077403980961129560273660186 absolute error = 2.640077403980961129560273660186 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.755 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.274 Order of pole (six term test) = -0.8029 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 0 y[1] (numeric) = 2.646272435038381328246103580801 absolute error = 2.646272435038381328246103580801 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.76 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 = 5.282 Order of pole (six term test) = -0.8031 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 0 y[1] (numeric) = 2.6524743066905361672951079804744 absolute error = 2.6524743066905361672951079804744 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.766 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.291 Order of pole (six term test) = -0.8033 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 0 y[1] (numeric) = 2.6586830458662109647317264620251 absolute error = 2.6586830458662109647317264620251 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.771 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 = 5.299 Order of pole (six term test) = -0.8035 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 0 y[1] (numeric) = 2.6648986795368163879060856555193 absolute error = 2.6648986795368163879060856555193 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.777 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.308 Order of pole (six term test) = -0.8037 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 0 y[1] (numeric) = 2.6711212347166808987093127985763 absolute error = 2.6711212347166808987093127985763 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.782 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 = 5.316 Order of pole (six term test) = -0.8039 TOP MAIN SOLVE Loop bytes used=156052692, alloc=4652204, time=5.49 x[1] = 4.92 y[1] (analytic) = 0 y[1] (numeric) = 2.6773507384633432603827702981538 absolute error = 2.6773507384633432603827702981538 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.788 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.325 Order of pole (six term test) = -0.8041 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 0 y[1] (numeric) = 2.6835872178778451127255851381681 absolute error = 2.6835872178778451127255851381681 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.793 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 = 5.333 Order of pole (six term test) = -0.8043 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 0 y[1] (numeric) = 2.6898307001050236224752098873177 absolute error = 2.6898307001050236224752098873177 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.799 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 = 5.342 Order of pole (six term test) = -0.8045 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 0 y[1] (numeric) = 2.6960812123338042156065332545541 absolute error = 2.6960812123338042156065332545541 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.804 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 = 5.35 Order of pole (six term test) = -0.8047 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 0 y[1] (numeric) = 2.702338781797493398266253449184 absolute error = 2.702338781797493398266253449184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.81 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 = 5.359 Order of pole (six term test) = -0.8049 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 0 y[1] (numeric) = 2.708603435774071673030832897127 absolute error = 2.708603435774071673030832897127 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.815 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.367 Order of pole (six term test) = -0.8051 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 0 y[1] (numeric) = 2.7148752015864865571483640673378 absolute error = 2.7148752015864865571483640673378 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.821 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 = 5.376 Order of pole (six term test) = -0.8053 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 0 y[1] (numeric) = 2.7211541066029457093970892493888 absolute error = 2.7211541066029457093970892493888 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.826 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.384 Order of pole (six term test) = -0.8055 Finished! diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3)); Iterations = 490 Total Elapsed Time = 5 Seconds Elapsed Time(since restart) = 5 Seconds Time to Timeout = 2 Minutes 54 Seconds Percent Done = 100.2 % > quit bytes used=158481356, alloc=4652204, time=5.57