|\^/| 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_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre tanh $eq_no = 1 > array_tmp4_a1[1] := sinh(array_tmp3[1]); > array_tmp4_a2[1] := cosh(array_tmp3[1]); > array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[2] := att(1,array_tmp4_a1,array_tmp3,1); > array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[3] := att(2,array_tmp4_a1,array_tmp3,1); > array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[4] := att(3,array_tmp4_a1,array_tmp3,1); > array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre tanh $eq_no = 1 > array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[5] := att(4,array_tmp4_a1,array_tmp3,1); > array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[kkk] := att(kkk-1,array_tmp4_a1,array_tmp3,1); > array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_a1[1] := sinh(array_tmp3[1]); array_tmp4_a2[1] := cosh(array_tmp3[1]); array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[2] := att(1, array_tmp4_a1, array_tmp3, 1); array_tmp4[2] := ( array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[3] := att(2, array_tmp4_a1, array_tmp3, 1); array_tmp4[3] := ( array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[4] := att(3, array_tmp4_a1, array_tmp3, 1); array_tmp4[4] := ( array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[5] := att(4, array_tmp4_a1, array_tmp3, 1); array_tmp4[5] := ( array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[kkk] := att(kkk - 1, array_tmp4_a1, array_tmp3, 1); array_tmp4[kkk] := ( array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(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_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/tanh_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"); > 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_g:= Array(0..(max_terms + 1),[]); > array_tmp4_a1:= Array(0..(max_terms + 1),[]); > array_tmp4_a2:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_3D0[1] := 3.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 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 ) = tanh(sqrt(2.0*x + 3.0));"); > 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,"2013-05-26T05:29:04-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tanh_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));") > ; > 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,"tanh_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"tanh_sqrt maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/tanh_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"); 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_g := Array(0 .. max_terms + 1, []); array_tmp4_a1 := Array(0 .. max_terms + 1, []); array_tmp4_a2 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a1[term] := 0.; term := term + 1 end do; array_tmp4_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a2[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 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 ) = tanh(sqrt(2.0*x + 3.0));"); 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, "2013-05-26T05:29:04-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tanh_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));"); 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, "tanh_sqrt diffeq.mxt"); logitem_str(html_log_file, "tanh_sqrt maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/tanh_sqrtpostode.ode################# diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0)); ! #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 = 1.3441454810443660492218885643395e-165 estimated_step_error = 1.3441454810443660492218885643395e-165 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.0204050799970995785261903090292e-158 estimated_step_error = 9.0204050799970995785261903090292e-158 best_h = 4.00e-06 opt_iter = 3 bytes used=4000616, alloc=2883056, time=0.28 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.0534879570296586772398458897117e-150 estimated_step_error = 6.0534879570296586772398458897117e-150 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.0624224096248755985942030517609e-142 estimated_step_error = 4.0624224096248755985942030517609e-142 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 = 2.7262393684489029510297946944593e-134 estimated_step_error = 2.7262393684489029510297946944593e-134 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 = 1.8295400002751677055238188886066e-126 estimated_step_error = 1.8295400002751677055238188886066e-126 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 = 1.2277724112080545945639910186011e-118 estimated_step_error = 1.2277724112080545945639910186011e-118 best_h = 0.000128 opt_iter = 8 bytes used=8001712, alloc=3931440, time=0.56 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.2392922070732943093274398802390e-111 estimated_step_error = 8.2392922070732943093274398802390e-111 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.5290954690868474707224568245584e-103 estimated_step_error = 5.5290954690868474707224568245584e-103 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.7102448428554323100779449740857e-95 estimated_step_error = 3.7102448428554323100779449740857e-95 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 = 2.4895431165874853931993755416428e-87 estimated_step_error = 2.4895431165874853931993755416428e-87 best_h = 0.002048 opt_iter = 12 bytes used=12002740, alloc=4128012, time=0.86 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6702210652792571703646141730979e-79 estimated_step_error = 1.6702210652792571703646141730979e-79 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1202186245625089675705095988165e-71 estimated_step_error = 1.1202186245625089675705095988165e-71 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.5089810409001970284828312911833e-64 estimated_step_error = 7.5089810409001970284828312911833e-64 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.0275840051265146466699765871287e-56 estimated_step_error = 5.0275840051265146466699765871287e-56 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.3584840595164694456205455792571e-48 estimated_step_error = 3.3584840595164694456205455792571e-48 best_h = 0.065536 opt_iter = 17 bytes used=16003520, alloc=4193536, time=1.17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.2333699855337776852240734087567e-40 estimated_step_error = 2.2333699855337776852240734087567e-40 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 = 1.4721022290633497291558764157676e-32 estimated_step_error = 1.4721022290633497291558764157676e-32 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 = 1.806 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 = 2.202 Order of pole (six term test) = -0.4372 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0 y[1] (numeric) = 0.0094593381004985954826601201816836 absolute error = 0.0094593381004985954826601201816836 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.817 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 = 2.216 Order of pole (six term test) = -0.4326 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0 y[1] (numeric) = 0.018924508505127767640193031685038 absolute error = 0.018924508505127767640193031685038 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.829 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.23 Order of pole (six term test) = -0.4273 TOP MAIN SOLVE Loop bytes used=20004976, alloc=4259060, time=1.48 x[1] = 0.13 y[1] (analytic) = 0 y[1] (numeric) = 0.028395432263158646197743615872164 absolute error = 0.028395432263158646197743615872164 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.245 Order of pole (six term test) = -0.4212 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0 y[1] (numeric) = 0.037872031748748671402376307987138 absolute error = 0.037872031748748671402376307987138 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.851 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.261 Order of pole (six term test) = -0.4141 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0 y[1] (numeric) = 0.047354230633830724064787478470808 absolute error = 0.047354230633830724064787478470808 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.863 Order 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) = -0.4055 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0 y[1] (numeric) = 0.056841953861666999718122852049415 absolute error = 0.056841953861666999718122852049415 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.874 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.295 Order of pole (six term test) = -0.3952 TOP MAIN SOLVE Loop bytes used=24005656, alloc=4324584, time=1.79 x[1] = 0.17 y[1] (analytic) = 0 y[1] (numeric) = 0.066335127621048416388199497381673 absolute error = 0.066335127621048416388199497381673 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 = 2.315 Order of pole (six term test) = -0.3825 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0 y[1] (numeric) = 0.075833679321120990162842049045725 absolute error = 0.075833679321120990162842049045725 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.897 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.337 Order of pole (six term test) = -0.3664 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0 y[1] (numeric) = 0.085337537566821232645635838403177 absolute error = 0.085337537566821232645635838403177 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.908 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.362 Order of pole (six term test) = -0.3455 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.094846632134903220561373955674941 absolute error = 0.094846632134903220561373955674941 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.392 Order of pole (six term test) = -0.317 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0 y[1] (numeric) = 0.10436089395054056127429279863007 absolute error = 0.10436089395054056127429279863007 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=28006872, alloc=4324584, time=2.10 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.931 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.431 Order of pole (six term test) = -0.2763 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0 y[1] (numeric) = 0.11388025506448702976343427646557 absolute error = 0.11388025506448702976343427646557 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.943 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 = 2.485 Order of pole (six term test) = -0.2128 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0 y[1] (numeric) = 0.12340464863078018360253372766059 absolute error = 0.12340464863078018360253372766059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.954 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 = 2.57 Order of pole (six term test) = -0.1006 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0 y[1] (numeric) = 0.13293400888497277360043827278055 absolute error = 0.13293400888497277360043827278055 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.965 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 = 2.741 Order of pole (six term test) = 0.1518 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0 y[1] (numeric) = 0.14246827112287725981565357397372 absolute error = 0.14246827112287725981565357397372 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.977 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.36 Order of pole (six term test) = 1.243 TOP MAIN SOLVE Loop bytes used=32007740, alloc=4324584, time=2.41 x[1] = 0.26 y[1] (analytic) = 0 y[1] (numeric) = 0.15200737167980921646859558455708 absolute error = 0.15200737167980921646859558455708 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.988 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0 y[1] (numeric) = 0.16155124791031586560294973042079 absolute error = 0.16155124791031586560294973042079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 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 = 1.689 Order of pole (six term test) = -1.257 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0 y[1] (numeric) = 0.17109983816837641892272604620079 absolute error = 0.17109983816837641892272604620079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.011 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.993 Order of pole (six term test) = -0.9433 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0 y[1] (numeric) = 0.18065308178806133074958168002429 absolute error = 0.18065308178806133074958168002429 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 = 2.112 Order of pole (six term test) = -0.8143 TOP MAIN SOLVE Loop bytes used=36008908, alloc=4390108, time=2.72 x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.19021091906463797316888733656982 absolute error = 0.19021091906463797316888733656982 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 = 2.18 Order of pole (six term test) = -0.7439 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0 y[1] (numeric) = 0.19977329123611063779532067429614 absolute error = 0.19977329123611063779532067429614 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.045 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.225 Order of pole (six term test) = -0.6996 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0 y[1] (numeric) = 0.20934014046518314779288039807363 absolute error = 0.20934014046518314779288039807363 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.057 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.259 Order of pole (six term test) = -0.6692 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0 y[1] (numeric) = 0.21891140982163272940593866350275 absolute error = 0.21891140982163272940593866350275 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.068 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.287 Order of pole (six term test) = -0.6469 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0 y[1] (numeric) = 0.22848704326508414484690006502808 absolute error = 0.22848704326508414484690006502808 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.08 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 = 2.311 Order of pole (six term test) = -0.63 TOP MAIN SOLVE Loop bytes used=40009844, alloc=4390108, time=3.04 x[1] = 0.35 y[1] (analytic) = 0 y[1] (numeric) = 0.23806698562817342846695222656459 absolute error = 0.23806698562817342846695222656459 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.091 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 = 2.331 Order of pole (six term test) = -0.6167 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0 y[1] (numeric) = 0.2476511826000908962103885371528 absolute error = 0.2476511826000908962103885371528 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.103 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.35 Order of pole (six term test) = -0.6059 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0 y[1] (numeric) = 0.25723958071049341489872284282348 absolute error = 0.25723958071049341489872284282348 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.114 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.367 Order of pole (six term test) = -0.597 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0 y[1] (numeric) = 0.26683212731377622336563041849995 absolute error = 0.26683212731377622336563041849995 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.125 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.383 Order of pole (six term test) = -0.5896 TOP MAIN SOLVE Loop bytes used=44010728, alloc=4390108, time=3.35 x[1] = 0.39 y[1] (analytic) = 0 y[1] (numeric) = 0.27642877057369489230469079469626 absolute error = 0.27642877057369489230469079469626 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.398 Order of pole (six term test) = -0.5832 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.28602945944832829431674378722383 absolute error = 0.28602945944832829431674378722383 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.148 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.413 Order of pole (six term test) = -0.5777 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0 y[1] (numeric) = 0.29563414367537373045182695827513 absolute error = 0.29563414367537373045182695827513 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 = 2.427 Order of pole (six term test) = -0.573 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0 y[1] (numeric) = 0.30524277375776562491411800061105 absolute error = 0.30524277375776562491411800061105 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 = 2.44 Order of pole (six term test) = -0.5688 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0 y[1] (numeric) = 0.31485530094960945590243139181776 absolute error = 0.31485530094960945590243139181776 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.183 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.454 Order of pole (six term test) = -0.5651 TOP MAIN SOLVE Loop bytes used=48011516, alloc=4390108, time=3.66 x[1] = 0.44 y[1] (analytic) = 0 y[1] (numeric) = 0.32447167724242283814318161780193 absolute error = 0.32447167724242283814318161780193 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.194 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.467 Order of pole (six term test) = -0.5618 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0 y[1] (numeric) = 0.33409185535167591187184320551523 absolute error = 0.33409185535167591187184320551523 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.206 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 = 2.479 Order of pole (six term test) = -0.5588 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0 y[1] (numeric) = 0.34371578870362342415299726685656 absolute error = 0.34371578870362342415299726685656 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.217 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 = 2.492 Order of pole (six term test) = -0.5561 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0 y[1] (numeric) = 0.35334343142242111180459011639801 absolute error = 0.35334343142242111180459011639801 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.228 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 = 2.504 Order of pole (six term test) = -0.5537 TOP MAIN SOLVE Loop bytes used=52012364, alloc=4390108, time=3.98 x[1] = 0.48 y[1] (analytic) = 0 y[1] (numeric) = 0.36297473831751921110256930561015 absolute error = 0.36297473831751921110256930561015 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.516 Order of pole (six term test) = -0.5515 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0 y[1] (numeric) = 0.37260966487132612816873718190928 absolute error = 0.37260966487132612816873718190928 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.251 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.528 Order of pole (six term test) = -0.5495 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.38224816722713550575678583899844 absolute error = 0.38224816722713550575678583899844 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.263 Order 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) = -0.5476 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0 y[1] (numeric) = 0.39189020217731011730709668204362 absolute error = 0.39189020217731011730709668204362 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.274 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.551 Order of pole (six term test) = -0.5459 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0 y[1] (numeric) = 0.4015357271517162078873035800369 absolute error = 0.4015357271517162078873035800369 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 = 2.563 Order of pole (six term test) = -0.5443 TOP MAIN SOLVE Loop bytes used=56013192, alloc=4390108, time=4.29 x[1] = 0.53 y[1] (analytic) = 0 y[1] (numeric) = 0.41118470020640208420988077531185 absolute error = 0.41118470020640208420988077531185 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 = 2.574 Order of pole (six term test) = -0.5428 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0 y[1] (numeric) = 0.42083708001251493254739472549063 absolute error = 0.42083708001251493254739472549063 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.309 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.586 Order of pole (six term test) = -0.5414 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0 y[1] (numeric) = 0.43049282584545001426848790485425 absolute error = 0.43049282584545001426848790485425 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.597 Order of pole (six term test) = -0.5401 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0 y[1] (numeric) = 0.44015189757422655410216702524936 absolute error = 0.44015189757422655410216702524936 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.332 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 = 2.609 Order of pole (six term test) = -0.5389 TOP MAIN SOLVE Loop bytes used=60013968, alloc=4390108, time=4.60 x[1] = 0.57 y[1] (analytic) = 0 y[1] (numeric) = 0.44981425565108479630506545859128 absolute error = 0.44981425565108479630506545859128 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.343 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 = 2.62 Order of pole (six term test) = -0.5378 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0 y[1] (numeric) = 0.45947986110129885884843261808437 absolute error = 0.45947986110129885884843261808437 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.355 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 = 2.631 Order of pole (six term test) = -0.5367 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0 y[1] (numeric) = 0.46914867551320016574330387868113 absolute error = 0.46914867551320016574330387868113 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.366 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 = 2.642 Order of pole (six term test) = -0.5357 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.47882066102840638286084099671665 absolute error = 0.47882066102840638286084099671665 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.378 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.653 Order of pole (six term test) = -0.5348 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0 y[1] (numeric) = 0.48849578033225092325033729171599 absolute error = 0.48849578033225092325033729171599 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.389 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.664 Order of pole (six term test) = -0.5339 TOP MAIN SOLVE Loop bytes used=64014876, alloc=4455632, time=4.92 x[1] = 0.62 y[1] (analytic) = 0 y[1] (numeric) = 0.49817399664440822417321422410108 absolute error = 0.49817399664440822417321422410108 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 = 2.675 Order of pole (six term test) = -0.5331 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0 y[1] (numeric) = 0.50785527370971013001438229746865 absolute error = 0.50785527370971013001438229746865 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 = 2.686 Order of pole (six term test) = -0.5323 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0 y[1] (numeric) = 0.51753957578914884305329456010142 absolute error = 0.51753957578914884305329456010142 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.424 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.697 Order of pole (six term test) = -0.5315 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0 y[1] (numeric) = 0.52722686765106202792065970990518 absolute error = 0.52722686765106202792065970990518 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.435 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.708 Order of pole (six term test) = -0.5308 TOP MAIN SOLVE Loop bytes used=68015832, alloc=4455632, time=5.23 x[1] = 0.66 y[1] (analytic) = 0 y[1] (numeric) = 0.53691711456249577557221448420373 absolute error = 0.53691711456249577557221448420373 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.447 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 = 2.719 Order of pole (six term test) = -0.5301 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0 y[1] (numeric) = 0.54661028228074124891187322581841 absolute error = 0.54661028228074124891187322581841 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.458 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 = 2.73 Order of pole (six term test) = -0.5294 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0 y[1] (numeric) = 0.55630633704504094492148205258085 absolute error = 0.55630633704504094492148205258085 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.469 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 = 2.741 Order of pole (six term test) = -0.5288 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0 y[1] (numeric) = 0.56600524556846061742684810365333 absolute error = 0.56600524556846061742684810365333 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.481 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 = 2.752 Order of pole (six term test) = -0.5282 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.5757069750299230105684812155902 absolute error = 0.5757069750299230105684812155902 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.492 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 = 2.762 Order of pole (six term test) = -0.5276 TOP MAIN SOLVE Loop bytes used=72016744, alloc=4455632, time=5.54 x[1] = 0.71 y[1] (analytic) = 0 y[1] (numeric) = 0.58541149306639965576481639750987 absolute error = 0.58541149306639965576481639750987 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.504 Order 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) = -0.5271 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0 y[1] (numeric) = 0.59511876776525708456546335586711 absolute error = 0.59511876776525708456546335586711 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.515 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.784 Order of pole (six term test) = -0.5266 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0 y[1] (numeric) = 0.60482876765675390639796273829035 absolute error = 0.60482876765675390639796273829035 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 = 2.795 Order of pole (six term test) = -0.5261 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0 y[1] (numeric) = 0.61454146170668529391532739044028 absolute error = 0.61454146170668529391532739044028 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 = 2.805 Order of pole (six term test) = -0.5256 TOP MAIN SOLVE Loop bytes used=76017524, alloc=4455632, time=5.86 x[1] = 0.75 y[1] (analytic) = 0 y[1] (numeric) = 0.62425681930917150955118841504449 absolute error = 0.62425681930917150955118841504449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.816 Order of pole (six term test) = -0.5251 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0 y[1] (numeric) = 0.63397481027958719507885521052329 absolute error = 0.63397481027958719507885521052329 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.561 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.827 Order of pole (six term test) = -0.5247 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0 y[1] (numeric) = 0.64369540484762823154072042458552 absolute error = 0.64369540484762823154072042458552 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.573 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 = 2.838 Order of pole (six term test) = -0.5242 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0 y[1] (numeric) = 0.65341857365051305995250401171891 absolute error = 0.65341857365051305995250401171891 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.584 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 = 2.848 Order of pole (six term test) = -0.5238 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0 y[1] (numeric) = 0.66314428772631543377690774150833 absolute error = 0.66314428772631543377690774150833 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.596 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 = 2.859 Order of pole (six term test) = -0.5234 TOP MAIN SOLVE Loop bytes used=80018832, alloc=4455632, time=6.17 x[1] = 0.8 y[1] (analytic) = 0 y[1] (numeric) = 0.67287251850742565238431065441871 absolute error = 0.67287251850742565238431065441871 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.607 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 = 2.87 Order of pole (six term test) = -0.523 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0 y[1] (numeric) = 0.68260323781413740065216733116174 absolute error = 0.68260323781413740065216733116174 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.619 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.88 Order of pole (six term test) = -0.5227 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0 y[1] (numeric) = 0.69233641784835739357490761900255 absolute error = 0.69233641784835739357490761900255 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 = 2.891 Order of pole (six term test) = -0.5223 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0 y[1] (numeric) = 0.70207203118743509633477024091084 absolute error = 0.70207203118743509633477024091084 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 = 2.901 Order of pole (six term test) = -0.522 TOP MAIN SOLVE Loop bytes used=84019716, alloc=4455632, time=6.49 x[1] = 0.84 y[1] (analytic) = 0 y[1] (numeric) = 0.71181005077810985979089384848292 absolute error = 0.71181005077810985979089384848292 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.654 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.912 Order of pole (six term test) = -0.5217 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0 y[1] (numeric) = 0.72155044993057287884637214031855 absolute error = 0.72155044993057287884637214031855 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.665 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.923 Order of pole (six term test) = -0.5213 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0 y[1] (numeric) = 0.73129320231264144671566429961438 absolute error = 0.73129320231264144671566429961438 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.677 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 = 2.933 Order of pole (six term test) = -0.521 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0 y[1] (numeric) = 0.74103828194404304180021936319238 absolute error = 0.74103828194404304180021936319238 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.688 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 = 2.944 Order of pole (six term test) = -0.5207 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0 y[1] (numeric) = 0.75078566319080684574866812136545 absolute error = 0.75078566319080684574866812136545 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.7 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 = 2.955 Order of pole (six term test) = -0.5204 bytes used=88021980, alloc=4455632, time=6.80 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0 y[1] (numeric) = 0.76053532075976035138755565102848 absolute error = 0.76053532075976035138755565102848 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.711 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 = 2.965 Order of pole (six term test) = -0.5202 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0 y[1] (numeric) = 0.77028722969312877761536490077257 absolute error = 0.77028722969312877761536490077257 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.723 Order 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) = -0.5199 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0 y[1] (numeric) = 0.78004136536323506511056737814094 absolute error = 0.78004136536323506511056737814094 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.734 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.986 Order of pole (six term test) = -0.5196 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0 y[1] (numeric) = 0.78979770346729828186577597157098 absolute error = 0.78979770346729828186577597157098 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 = 2.997 Order of pole (six term test) = -0.5194 TOP MAIN SOLVE Loop bytes used=92022660, alloc=4455632, time=7.13 x[1] = 0.93 y[1] (analytic) = 0 y[1] (numeric) = 0.79955622002232832117508087377279 absolute error = 0.79955622002232832117508087377279 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 = 3.007 Order of pole (six term test) = -0.5192 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0 y[1] (numeric) = 0.80931689136011482681887550640978 absolute error = 0.80931689136011482681887550640978 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.769 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.018 Order of pole (six term test) = -0.5189 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0 y[1] (numeric) = 0.81907969412230833085678565131263 absolute error = 0.81907969412230833085678565131263 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.029 Order of pole (six term test) = -0.5187 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0 y[1] (numeric) = 0.82884460525559163869993438645545 absolute error = 0.82884460525559163869993438645545 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.792 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 = 3.039 Order of pole (six term test) = -0.5185 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0 y[1] (numeric) = 0.83861160200693954403237524628494 absolute error = 0.83861160200693954403237524628494 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.803 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 = 3.05 Order of pole (six term test) = -0.5183 bytes used=96027836, alloc=4455632, time=7.44 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0 y[1] (numeric) = 0.84838066191896500273026791747588 absolute error = 0.84838066191896500273026791747588 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.815 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 = 3.06 Order of pole (six term test) = -0.5181 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0 y[1] (numeric) = 0.85815176282534994022696787232501 absolute error = 0.85815176282534994022696787232501 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.826 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 = 3.071 Order of pole (six term test) = -0.5179 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0 y[1] (numeric) = 0.86792488284635891083197306080736 absolute error = 0.86792488284635891083197306080736 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.838 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.081 Order of pole (six term test) = -0.5177 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0 y[1] (numeric) = 0.87770000038443387036959539728858 absolute error = 0.87770000038443387036959539728858 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.849 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.092 Order of pole (six term test) = -0.5175 TOP MAIN SOLVE Loop bytes used=100028644, alloc=4455632, time=7.75 x[1] = 1.02 y[1] (analytic) = 0 y[1] (numeric) = 0.88747709411986836519598977333318 absolute error = 0.88747709411986836519598977333318 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 = 3.102 Order of pole (six term test) = -0.5174 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0 y[1] (numeric) = 0.89725614300655948121622370999137 absolute error = 0.89725614300655948121622370999137 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 = 3.113 Order of pole (six term test) = -0.5172 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0 y[1] (numeric) = 0.90703712626783593599065538790119 absolute error = 0.90703712626783593599065538790119 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.884 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.123 Order of pole (six term test) = -0.5171 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0 y[1] (numeric) = 0.91682002339236073542510380818754 absolute error = 0.91682002339236073542510380818754 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.895 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.134 Order of pole (six term test) = -0.5169 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0 y[1] (numeric) = 0.92660481413010685391413031260164 absolute error = 0.92660481413010685391413031260164 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.907 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 = 3.144 Order of pole (six term test) = -0.5168 bytes used=104030612, alloc=4455632, time=8.07 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0 y[1] (numeric) = 0.93639147848840443318212553179931 absolute error = 0.93639147848840443318212553179931 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.918 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 = 3.155 Order of pole (six term test) = -0.5166 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0 y[1] (numeric) = 0.94617999672805803047270103217014 absolute error = 0.94617999672805803047270103217014 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.165 Order of pole (six term test) = -0.5165 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0 y[1] (numeric) = 0.95597034935953248120202026353444 absolute error = 0.95597034935953248120202026353444 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.942 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.176 Order of pole (six term test) = -0.5164 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.96576251713920597474411358771586 absolute error = 0.96576251713920597474411358771586 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.953 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.186 Order of pole (six term test) = -0.5163 TOP MAIN SOLVE Loop bytes used=108031416, alloc=4521156, time=8.39 x[1] = 1.11 y[1] (analytic) = 0 y[1] (numeric) = 0.97555648106568897468293158276567 absolute error = 0.97555648106568897468293158276567 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 = 3.197 Order of pole (six term test) = -0.5162 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0 y[1] (numeric) = 0.98535222237620764667303688607237 absolute error = 0.98535222237620764667303688607237 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 = 3.207 Order of pole (six term test) = -0.5161 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0 y[1] (numeric) = 0.99514972254305048802370003228761 absolute error = 0.99514972254305048802370003228761 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.988 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.218 Order of pole (six term test) = -0.516 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0 y[1] (numeric) = 1.0049489632700768832842073480775 absolute error = 1.0049489632700768832842073480775 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.999 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.228 Order of pole (six term test) = -0.5159 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 0 y[1] (numeric) = 1.0147499264892863394850726477601 absolute error = 1.0147499264892863394850726477601 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.011 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.239 Order of pole (six term test) = -0.5158 bytes used=112033800, alloc=4521156, time=8.70 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0 y[1] (numeric) = 1.0245525943574471833034666647296 absolute error = 1.0245525943574471833034666647296 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.022 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.249 Order of pole (six term test) = -0.5157 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0 y[1] (numeric) = 1.0343569492527835302936973441727 absolute error = 1.0343569492527835302936973441727 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.034 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 = 3.26 Order of pole (six term test) = -0.5156 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0 y[1] (numeric) = 1.0441629737717193634764360882757 absolute error = 1.0441629737717193634764360882757 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.045 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.27 Order of pole (six term test) = -0.5156 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0 y[1] (numeric) = 1.0539706507256785850343480548076 absolute error = 1.0539706507256785850343480548076 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.057 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.281 Order of pole (six term test) = -0.5155 TOP MAIN SOLVE Loop bytes used=116034856, alloc=4521156, time=9.02 x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 1.0637799631379399306369436613221 absolute error = 1.0637799631379399306369436613221 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.068 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.291 Order of pole (six term test) = -0.5155 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0 y[1] (numeric) = 1.0735908942405456610332785686242 absolute error = 1.0735908942405456610332785686242 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 = 3.301 Order of pole (six term test) = -0.5154 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0 y[1] (numeric) = 1.0834034274712629700264280754662 absolute error = 1.0834034274712629700264280754662 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 = 3.312 Order of pole (six term test) = -0.5154 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0 y[1] (numeric) = 1.0932175464705970717966905078279 absolute error = 1.0932175464705970717966905078279 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.103 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.322 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0 y[1] (numeric) = 1.1030332350788549537888990055612 absolute error = 1.1030332350788549537888990055612 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.114 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.333 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop bytes used=120035752, alloc=4521156, time=9.33 x[1] = 1.25 y[1] (analytic) = 0 y[1] (numeric) = 1.1128504773332588040401529325035 absolute error = 1.1128504773332588040401529325035 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.126 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.343 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0 y[1] (numeric) = 1.1226692574651081439142936474008 absolute error = 1.1226692574651081439142936474008 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.354 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0 y[1] (numeric) = 1.1324895598969897187446015676407 absolute error = 1.1324895598969897187446015676407 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.149 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 = 3.364 Order of pole (six term test) = -0.5152 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0 y[1] (numeric) = 1.1423113692400342198820394120326 absolute error = 1.1423113692400342198820394120326 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.161 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.375 Order of pole (six term test) = -0.5152 TOP MAIN SOLVE Loop bytes used=124036732, alloc=4521156, time=9.64 x[1] = 1.29 y[1] (analytic) = 0 y[1] (numeric) = 1.1521346702912189321179844827172 absolute error = 1.1521346702912189321179844827172 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.172 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.385 Order of pole (six term test) = -0.5152 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 1.1619594480307154204123887481079 absolute error = 1.1619594480307154204123887481079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.184 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 = 3.396 Order of pole (six term test) = -0.5152 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0 y[1] (numeric) = 1.1717856876192813893248367267776 absolute error = 1.1717856876192813893248367267776 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.195 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 = 3.406 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0 y[1] (numeric) = 1.1816133743956958675307599178874 absolute error = 1.1816133743956958675307599178874 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 = 3.416 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0 y[1] (numeric) = 1.1914424938742368883214144107534 absolute error = 1.1914424938742368883214144107534 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.218 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.427 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop bytes used=128037640, alloc=4521156, time=9.96 x[1] = 1.34 y[1] (analytic) = 0 y[1] (numeric) = 1.2012730317422008550470305874214 absolute error = 1.2012730317422008550470305874214 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.437 Order of pole (six term test) = -0.5153 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0 y[1] (numeric) = 1.2111049738574627980803030168932 absolute error = 1.2111049738574627980803030168932 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.241 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.448 Order of pole (six term test) = -0.5154 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0 y[1] (numeric) = 1.2209383062460767470642276310155 absolute error = 1.2209383062460767470642276310155 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.253 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.458 Order of pole (six term test) = -0.5154 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0 y[1] (numeric) = 1.2307730150999154589759680249779 absolute error = 1.2307730150999154589759680249779 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.264 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.469 Order of pole (six term test) = -0.5154 TOP MAIN SOLVE Loop bytes used=132038656, alloc=4521156, time=10.28 x[1] = 1.38 y[1] (analytic) = 0 y[1] (numeric) = 1.2406090867743487588983444441873 absolute error = 1.2406090867743487588983444441873 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.276 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.479 Order of pole (six term test) = -0.5155 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0 y[1] (numeric) = 1.2504465077859597663537459127207 absolute error = 1.2504465077859597663537459127207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.287 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.489 Order of pole (six term test) = -0.5156 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 1.2602852648102982956324945698509 absolute error = 1.2602852648102982956324945698509 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.299 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 = 3.5 Order of pole (six term test) = -0.5156 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0 y[1] (numeric) = 1.2701253446796707337493474098215 absolute error = 1.2701253446796707337493474098215 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.31 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 = 3.51 Order of pole (six term test) = -0.5157 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0 y[1] (numeric) = 1.2799667343809657144979998513758 absolute error = 1.2799667343809657144979998513758 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 = 3.521 Order of pole (six term test) = -0.5158 TOP MAIN SOLVE Loop bytes used=136039648, alloc=4521156, time=10.59 x[1] = 1.43 y[1] (analytic) = 0 y[1] (numeric) = 1.2898094210535149215539534208783 absolute error = 1.2898094210535149215539534208783 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 = 3.531 Order of pole (six term test) = -0.5159 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0 y[1] (numeric) = 1.2996533919869883677104315676126 absolute error = 1.2996533919869883677104315676126 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.345 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.542 Order of pole (six term test) = -0.5159 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0 y[1] (numeric) = 1.3094986346193235111293976630234 absolute error = 1.3094986346193235111293976630234 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.356 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.552 Order of pole (six term test) = -0.516 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0 y[1] (numeric) = 1.319345136534687582959100264573 absolute error = 1.319345136534687582959100264573 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.368 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 = 3.562 Order of pole (six term test) = -0.5162 TOP MAIN SOLVE Loop bytes used=140041152, alloc=4521156, time=10.91 x[1] = 1.47 y[1] (analytic) = 0 y[1] (numeric) = 1.3291928854614725138196325076093 absolute error = 1.3291928854614725138196325076093 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.379 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 = 3.573 Order of pole (six term test) = -0.5163 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0 y[1] (numeric) = 1.3390418692703218594971803189922 absolute error = 1.3390418692703218594971803189922 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.391 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.583 Order of pole (six term test) = -0.5164 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0 y[1] (numeric) = 1.3488920759721891387241370307101 absolute error = 1.3488920759721891387241370307101 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.402 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.594 Order of pole (six term test) = -0.5165 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 1.3587434937164270081640305200396 absolute error = 1.3587434937164270081640305200396 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.414 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 = 3.604 Order of pole (six term test) = -0.5166 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 0 y[1] (numeric) = 1.3685961107889067116749630427342 absolute error = 1.3685961107889067116749630427342 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.425 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 = 3.615 Order of pole (six term test) = -0.5168 TOP MAIN SOLVE Loop bytes used=144041820, alloc=4521156, time=11.23 x[1] = 1.52 y[1] (analytic) = 0 y[1] (numeric) = 1.3784499156101672526004998527908 absolute error = 1.3784499156101672526004998527908 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 = 3.625 Order of pole (six term test) = -0.5169 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 0 y[1] (numeric) = 1.3883048967335937492399405742862 absolute error = 1.3883048967335937492399405742862 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 = 3.635 Order of pole (six term test) = -0.5171 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0 y[1] (numeric) = 1.3981610428436244447877376765368 absolute error = 1.3981610428436244447877376765368 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.646 Order of pole (six term test) = -0.5172 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0 y[1] (numeric) = 1.4080183427539858539113569960737 absolute error = 1.4080183427539858539113569960737 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.471 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.656 Order of pole (six term test) = -0.5174 TOP MAIN SOLVE Loop bytes used=148043104, alloc=4521156, time=11.54 x[1] = 1.56 y[1] (analytic) = 0 y[1] (numeric) = 1.4178767854059555387647772490946 absolute error = 1.4178767854059555387647772490946 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.483 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 = 3.667 Order of pole (six term test) = -0.5176 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0 y[1] (numeric) = 1.4277363598666520176175797624253 absolute error = 1.4277363598666520176175797624253 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.494 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 = 3.677 Order of pole (six term test) = -0.5177 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0 y[1] (numeric) = 1.437597055327351319423482725791 absolute error = 1.437597055327351319423482725791 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.506 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.687 Order of pole (six term test) = -0.5179 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 0 y[1] (numeric) = 1.4474588611018297075633440215725 absolute error = 1.4474588611018297075633440215725 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.517 Order 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) = -0.5181 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 1.4573217666247321056820379468978 absolute error = 1.4573217666247321056820379468978 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.529 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 = 3.708 Order of pole (six term test) = -0.5183 TOP MAIN SOLVE Loop bytes used=152044112, alloc=4521156, time=11.86 x[1] = 1.61 y[1] (analytic) = 0 y[1] (numeric) = 1.4671857614499657680019810402239 absolute error = 1.4671857614499657680019810402239 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.54 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 = 3.719 Order of pole (six term test) = -0.5185 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0 y[1] (numeric) = 1.4770508352491187457440553871414 absolute error = 1.4770508352491187457440553871414 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 = 3.729 Order of pole (six term test) = -0.5187 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0 y[1] (numeric) = 1.4869169778099027103247113398399 absolute error = 1.4869169778099027103247113398399 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 = 3.74 Order of pole (six term test) = -0.5189 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0 y[1] (numeric) = 1.4967841790346197028314300220635 absolute error = 1.4967841790346197028314300220635 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.575 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.75 Order of pole (six term test) = -0.5192 TOP MAIN SOLVE Loop bytes used=156045092, alloc=4521156, time=12.17 x[1] = 1.65 y[1] (analytic) = 0 y[1] (numeric) = 1.5066524289386523879126458169135 absolute error = 1.5066524289386523879126458169135 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.586 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.76 Order of pole (six term test) = -0.5194 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0 y[1] (numeric) = 1.516521717648977398657683313669 absolute error = 1.516521717648977398657683313669 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.598 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 = 3.771 Order of pole (six term test) = -0.5197 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 0 y[1] (numeric) = 1.5263920354027013672921259158465 absolute error = 1.5263920354027013672921259158465 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.609 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 = 3.781 Order of pole (six term test) = -0.5199 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0 y[1] (numeric) = 1.536263372545619244579043637507 absolute error = 1.536263372545619244579043637507 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.621 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.792 Order of pole (six term test) = -0.5202 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0 y[1] (numeric) = 1.5461357195307945187012739361634 absolute error = 1.5461357195307945187012739361634 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.632 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.802 Order of pole (six term test) = -0.5204 TOP MAIN SOLVE Loop bytes used=160045916, alloc=4521156, time=12.49 x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 1.5560090669171609521089533463316 absolute error = 1.5560090669171609521089533463316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.644 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 = 3.812 Order of pole (six term test) = -0.5207 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0 y[1] (numeric) = 1.5658834053681454623540978090601 absolute error = 1.5658834053681454623540978090601 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.655 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 = 3.823 Order of pole (six term test) = -0.521 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0 y[1] (numeric) = 1.5757587256503117803044652823162 absolute error = 1.5757587256503117803044652823162 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 = 3.833 Order of pole (six term test) = -0.5213 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0 y[1] (numeric) = 1.5856350186320245263363291057308 absolute error = 1.5856350186320245263363291057308 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 = 3.844 Order of pole (six term test) = -0.5216 TOP MAIN SOLVE Loop bytes used=164047532, alloc=4521156, time=12.80 x[1] = 1.74 y[1] (analytic) = 0 y[1] (numeric) = 1.595512275282133352154156079988 absolute error = 1.595512275282133352154156079988 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.854 Order of pole (six term test) = -0.5219 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0 y[1] (numeric) = 1.6053904866686768027784218107169 absolute error = 1.6053904866686768027784218107169 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.701 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.864 Order of pole (six term test) = -0.5222 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0 y[1] (numeric) = 1.6152696439576055599847044079647 absolute error = 1.6152696439576055599847044079647 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.713 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.875 Order of pole (six term test) = -0.5225 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0 y[1] (numeric) = 1.6251497384115247350714704520594 absolute error = 1.6251497384115247350714704520594 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.724 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.885 Order of pole (six term test) = -0.5228 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0 y[1] (numeric) = 1.6350307613884548852841990723315 absolute error = 1.6350307613884548852841990723315 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.735 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.896 Order of pole (six term test) = -0.5232 TOP MAIN SOLVE Loop bytes used=168048780, alloc=4521156, time=13.12 x[1] = 1.79 y[1] (analytic) = 0 y[1] (numeric) = 1.6449127043406114345331793196886 absolute error = 1.6449127043406114345331793196886 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.747 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.906 Order of pole (six term test) = -0.5235 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 1.654795558813202185214867316495 absolute error = 1.654795558813202185214867316495 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.758 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.916 Order of pole (six term test) = -0.5239 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 0 y[1] (numeric) = 1.6646793164432426139854165425218 absolute error = 1.6646793164432426139854165425218 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.77 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 = 3.927 Order of pole (six term test) = -0.5242 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0 y[1] (numeric) = 1.6745639689583886502431223665296 absolute error = 1.6745639689583886502431223665296 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.781 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 = 3.937 Order of pole (six term test) = -0.5246 TOP MAIN SOLVE Loop bytes used=172049740, alloc=4521156, time=13.44 x[1] = 1.83 y[1] (analytic) = 0 y[1] (numeric) = 1.6844495081757866418571901367256 absolute error = 1.6844495081757866418571901367256 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 = 3.948 Order of pole (six term test) = -0.525 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0 y[1] (numeric) = 1.6943359260009402183365011473086 absolute error = 1.6943359260009402183365011473086 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 = 3.958 Order of pole (six term test) = -0.5253 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 0 y[1] (numeric) = 1.7042232144265937671668881361422 absolute error = 1.7042232144265937671668881361422 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.816 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.968 Order of pole (six term test) = -0.5257 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0 y[1] (numeric) = 1.714111365531632244461738699845 absolute error = 1.714111365531632244461738699845 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.827 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.979 Order of pole (six term test) = -0.5261 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0 y[1] (numeric) = 1.7240003714799970463713419889124 absolute error = 1.7240003714799970463713419889124 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.839 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 = 3.989 Order of pole (six term test) = -0.5265 TOP MAIN SOLVE Loop bytes used=176050744, alloc=4521156, time=13.76 x[1] = 1.88 y[1] (analytic) = 0 y[1] (numeric) = 1.7338902245196176728840281055415 absolute error = 1.7338902245196176728840281055415 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.85 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 = 4 Order of pole (six term test) = -0.527 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0 y[1] (numeric) = 1.7437809169813589207294957223611 absolute error = 1.7437809169813589207294957223611 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.861 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 = 4.01 Order of pole (six term test) = -0.5274 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0 y[1] (numeric) = 1.7536724412779833470643866957529 absolute error = 1.7536724412779833470643866957529 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.873 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.02 Order of pole (six term test) = -0.5278 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0 y[1] (numeric) = 1.7635647899031287504846841555408 absolute error = 1.7635647899031287504846841555408 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.884 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.031 Order of pole (six term test) = -0.5283 TOP MAIN SOLVE Loop bytes used=180051572, alloc=4521156, time=14.08 x[1] = 1.92 y[1] (analytic) = 0 y[1] (numeric) = 1.7734579554303004206713541077481 absolute error = 1.7734579554303004206713541077481 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.896 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 = 4.041 Order of pole (six term test) = -0.5287 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 0 y[1] (numeric) = 1.7833519305118779126372273581047 absolute error = 1.7833519305118779126372273581047 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.907 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 = 4.052 Order of pole (six term test) = -0.5292 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0 y[1] (numeric) = 1.7932467078781361061067737107619 absolute error = 1.7932467078781361061067737107619 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.919 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.062 Order of pole (six term test) = -0.5297 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0 y[1] (numeric) = 1.8031422803362803150284386289666 absolute error = 1.8031422803362803150284386289666 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.072 Order of pole (six term test) = -0.5301 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0 y[1] (numeric) = 1.8130386407694952165938198273431 absolute error = 1.8130386407694952165938198273431 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.941 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.083 Order of pole (six term test) = -0.5306 TOP MAIN SOLVE Loop bytes used=184052840, alloc=4521156, time=14.40 x[1] = 1.97 y[1] (analytic) = 0 y[1] (numeric) = 1.8229357821360073734213264723789 absolute error = 1.8229357821360073734213264723789 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.953 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.093 Order of pole (six term test) = -0.5311 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0 y[1] (numeric) = 1.8328336974681611267562001829739 absolute error = 1.8328336974681611267562001829739 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.964 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.103 Order of pole (six term test) = -0.5316 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0 y[1] (numeric) = 1.842732379871507642645944295065 absolute error = 1.842732379871507642645944295065 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.976 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 = 4.114 Order of pole (six term test) = -0.5322 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.8526318225239068970723129024668 absolute error = 1.8526318225239068970723129024668 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.987 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 = 4.124 Order of pole (six term test) = -0.5327 TOP MAIN SOLVE Loop bytes used=188053656, alloc=4521156, time=14.71 x[1] = 2.01 y[1] (analytic) = 0 y[1] (numeric) = 1.8625320186746423899600100602514 absolute error = 1.8625320186746423899600100602514 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.998 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 = 4.135 Order of pole (six term test) = -0.5332 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0 y[1] (numeric) = 1.8724329616435483818400487344794 absolute error = 1.8724329616435483818400487344794 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.145 Order of pole (six term test) = -0.5338 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0 y[1] (numeric) = 1.8823346448201494507241769207718 absolute error = 1.8823346448201494507241769207718 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.021 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.155 Order of pole (six term test) = -0.5343 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0 y[1] (numeric) = 1.8922370616628121704477063045975 absolute error = 1.8922370616628121704477063045975 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.033 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.166 Order of pole (six term test) = -0.5349 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0 y[1] (numeric) = 1.9021402056979087153632428133803 absolute error = 1.9021402056979087153632428133803 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.044 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 = 4.176 Order of pole (six term test) = -0.5355 TOP MAIN SOLVE Loop bytes used=192054472, alloc=4521156, time=15.03 x[1] = 2.06 y[1] (analytic) = 0 y[1] (numeric) = 1.9120440705189921998189400276172 absolute error = 1.9120440705189921998189400276172 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.055 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 = 4.187 Order of pole (six term test) = -0.5361 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0 y[1] (numeric) = 1.9219486497859835643336542017604 absolute error = 1.9219486497859835643336542017604 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.067 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.197 Order of pole (six term test) = -0.5366 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0 y[1] (numeric) = 1.9318539372243698237894102153662 absolute error = 1.9318539372243698237894102153662 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.078 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.207 Order of pole (six term test) = -0.5372 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0 y[1] (numeric) = 1.9417599266244134963004869881377 absolute error = 1.9417599266244134963004869881377 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.218 Order of pole (six term test) = -0.5379 TOP MAIN SOLVE Loop bytes used=196055564, alloc=4521156, time=15.35 x[1] = 2.1 y[1] (analytic) = 0 y[1] (numeric) = 1.9516666118403730346897549540367 absolute error = 1.9516666118403730346897549540367 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.101 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = -0.5385 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0 y[1] (numeric) = 1.9615739867897340857081647300476 absolute error = 1.9615739867897340857081647300476 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.112 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.238 Order of pole (six term test) = -0.5391 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0 y[1] (numeric) = 1.9714820454524514052739752359584 absolute error = 1.9714820454524514052739752359584 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.124 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 = 4.249 Order of pole (six term test) = -0.5398 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0 y[1] (numeric) = 1.9813907818702012610858648101341 absolute error = 1.9813907818702012610858648101341 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.135 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 = 4.259 Order of pole (six term test) = -0.5404 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0 y[1] (numeric) = 1.991300190145644156979898381147 absolute error = 1.991300190145644156979898381147 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.147 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.27 Order of pole (six term test) = -0.5411 TOP MAIN SOLVE Loop bytes used=200057120, alloc=4521156, time=15.67 x[1] = 2.15 y[1] (analytic) = 0 y[1] (numeric) = 2.0012102644416977163558009818894 absolute error = 2.0012102644416977163558009818894 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.158 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.28 Order of pole (six term test) = -0.5417 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0 y[1] (numeric) = 2.0111209989808195648944526723583 absolute error = 2.0111209989808195648944526723583 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.169 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.29 Order of pole (six term test) = -0.5424 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0 y[1] (numeric) = 2.0210323880443000556272793670455 absolute error = 2.0210323880443000556272793670455 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.181 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 = 4.301 Order of pole (six term test) = -0.5431 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0 y[1] (numeric) = 2.0309444259715646822005433714902 absolute error = 2.0309444259715646822005433714902 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.192 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 = 4.311 Order of pole (six term test) = -0.5438 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0 y[1] (numeric) = 2.0408571071594860289046808295383 absolute error = 2.0408571071594860289046808295383 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=204058308, alloc=4521156, time=15.98 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.203 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 = 4.322 Order of pole (six term test) = -0.5445 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0 y[1] (numeric) = 2.0507704260617051087120047833663 absolute error = 2.0507704260617051087120047833663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.215 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.332 Order of pole (six term test) = -0.5453 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0 y[1] (numeric) = 2.0606843771879619431864767742034 absolute error = 2.0606843771879619431864767742034 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.226 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.342 Order of pole (six term test) = -0.546 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0 y[1] (numeric) = 2.0705989551034352406980028694012 absolute error = 2.0705989551034352406980028694012 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.237 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.353 Order of pole (six term test) = -0.5467 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0 y[1] (numeric) = 2.0805141544280910318919598377317 absolute error = 2.0805141544280910318919598377317 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.249 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.363 Order of pole (six term test) = -0.5475 TOP MAIN SOLVE Loop bytes used=208059380, alloc=4521156, time=16.30 x[1] = 2.24 y[1] (analytic) = 0 y[1] (numeric) = 2.090429969836040123833504930294 absolute error = 2.090429969836040123833504930294 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.373 Order of pole (six term test) = -0.5483 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0 y[1] (numeric) = 2.1003463960549042366667429669167 absolute error = 2.1003463960549042366667429669167 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.272 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 = 4.384 Order of pole (six term test) = -0.549 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0 y[1] (numeric) = 2.1102634278651906890020660646919 absolute error = 2.1102634278651906890020660646919 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.283 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 = 4.394 Order of pole (six term test) = -0.5498 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0 y[1] (numeric) = 2.1201810600996755005719682158104 absolute error = 2.1201810600996755005719682158104 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.294 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 = 4.404 Order of pole (six term test) = -0.5506 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 0 y[1] (numeric) = 2.130099287642794782977368471723 absolute error = 2.130099287642794782977368471723 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.306 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.415 Order of pole (six term test) = -0.5514 bytes used=212060756, alloc=4521156, time=16.61 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0 y[1] (numeric) = 2.1400181054300442915839284065133 absolute error = 2.1400181054300442915839284065133 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.317 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.425 Order of pole (six term test) = -0.5522 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0 y[1] (numeric) = 2.1499375084473870138219743592397 absolute error = 2.1499375084473870138219743592397 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.328 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.436 Order of pole (six term test) = -0.5531 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0 y[1] (numeric) = 2.1598574917306686712953626960059 absolute error = 2.1598574917306686712953626960059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.34 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 = 4.446 Order of pole (six term test) = -0.5539 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0 y[1] (numeric) = 2.169778050365041015214865031755 absolute error = 2.169778050365041015214865031755 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.351 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 = 4.456 Order of pole (six term test) = -0.5547 TOP MAIN SOLVE Loop bytes used=216061788, alloc=4521156, time=16.93 x[1] = 2.33 y[1] (analytic) = 0 y[1] (numeric) = 2.1796991794843927967412866608612 absolute error = 2.1796991794843927967412866608612 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.362 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 = 4.467 Order of pole (six term test) = -0.5556 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0 y[1] (numeric) = 2.1896208742707882958534311742777 absolute error = 2.1896208742707882958534311742777 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.374 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.477 Order of pole (six term test) = -0.5565 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0 y[1] (numeric) = 2.1995431299539132943470328924389 absolute error = 2.1995431299539132943470328924389 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.385 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.487 Order of pole (six term test) = -0.5574 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0 y[1] (numeric) = 2.2094659418105283805237220341877 absolute error = 2.2094659418105283805237220341877 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.396 Order 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) = -0.5583 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0 y[1] (numeric) = 2.2193893051639294750447719091272 absolute error = 2.2193893051639294750447719091272 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.407 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.508 Order of pole (six term test) = -0.5592 TOP MAIN SOLVE Loop bytes used=220062832, alloc=4521156, time=17.25 x[1] = 2.38 y[1] (analytic) = 0 y[1] (numeric) = 2.2293132153834154693035905117604 absolute error = 2.2293132153834154693035905117604 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.419 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.519 Order of pole (six term test) = -0.5601 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0 y[1] (numeric) = 2.2392376678837628695144300478953 absolute error = 2.2392376678837628695144300478953 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.529 Order of pole (six term test) = -0.561 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0 y[1] (numeric) = 2.2491626581247073415233486288436 absolute error = 2.2491626581247073415233486288436 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.441 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.539 Order of pole (six term test) = -0.5619 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0 y[1] (numeric) = 2.2590881816104320531218027253603 absolute error = 2.2590881816104320531218027253603 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.453 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.55 Order of pole (six term test) = -0.5629 TOP MAIN SOLVE Loop bytes used=224063632, alloc=4521156, time=17.57 x[1] = 2.42 y[1] (analytic) = 0 y[1] (numeric) = 2.2690142338890627123840941257992 absolute error = 2.2690142338890627123840941257992 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.464 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.56 Order of pole (six term test) = -0.5638 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0 y[1] (numeric) = 2.2789408105521692022579417103119 absolute error = 2.2789408105521692022579417103119 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.475 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.57 Order of pole (six term test) = -0.5648 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0 y[1] (numeric) = 2.2888679072342737133133808436781 absolute error = 2.2888679072342737133133808436781 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.487 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.581 Order of pole (six term test) = -0.5658 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0 y[1] (numeric) = 2.2987955196123652781996804065502 absolute error = 2.2987955196123652781996804065502 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.498 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.591 Order of pole (six term test) = -0.5668 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 0 y[1] (numeric) = 2.3087236434054206129736629195099 absolute error = 2.3087236434054206129736629195099 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.509 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.601 Order of pole (six term test) = -0.5678 TOP MAIN SOLVE Loop bytes used=228064496, alloc=4521156, time=17.88 x[1] = 2.47 y[1] (analytic) = 0 y[1] (numeric) = 2.3186522743739311720463554281373 absolute error = 2.3186522743739311720463554281373 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.612 Order of pole (six term test) = -0.5688 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 0 y[1] (numeric) = 2.3285814083194363250489118152737 absolute error = 2.3285814083194363250489118152737 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.532 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.622 Order of pole (six term test) = -0.5698 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 0 y[1] (numeric) = 2.3385110410840625654438407993632 absolute error = 2.3385110410840625654438407993632 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.543 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.632 Order of pole (six term test) = -0.5708 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0 y[1] (numeric) = 2.348441168550068662204344033852 absolute error = 2.348441168550068662204344033852 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.554 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.643 Order of pole (six term test) = -0.5719 TOP MAIN SOLVE Loop bytes used=232066024, alloc=4521156, time=18.20 x[1] = 2.51 y[1] (analytic) = 0 y[1] (numeric) = 2.3583717866393966673535979119389 absolute error = 2.3583717866393966673535979119389 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.566 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.653 Order of pole (six term test) = -0.5729 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0 y[1] (numeric) = 2.3683028913132286935976702083368 absolute error = 2.3683028913132286935976702083368 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.577 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.663 Order of pole (six term test) = -0.574 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 0 y[1] (numeric) = 2.3782344785715493777010050197882 absolute error = 2.3782344785715493777010050197882 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.588 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.674 Order of pole (six term test) = -0.5751 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0 y[1] (numeric) = 2.3881665444527139466425805395772 absolute error = 2.3881665444527139466425805395772 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.599 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.684 Order of pole (six term test) = -0.5762 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 0 y[1] (numeric) = 2.3980990850330218049544757426029 absolute error = 2.3980990850330218049544757426029 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.611 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.695 Order of pole (six term test) = -0.5772 TOP MAIN SOLVE Loop bytes used=236066820, alloc=4521156, time=18.51 x[1] = 2.56 y[1] (analytic) = 0 y[1] (numeric) = 2.4080320964262955629831938743774 absolute error = 2.4080320964262955629831938743774 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.622 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 = 4.705 Order of pole (six term test) = -0.5784 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0 y[1] (numeric) = 2.4179655747834654271281909120001 absolute error = 2.4179655747834654271281909120001 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.633 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 = 4.715 Order of pole (six term test) = -0.5795 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 0 y[1] (numeric) = 2.4278995162921588744021427387288 absolute error = 2.4278995162921588744021427387288 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.644 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.726 Order of pole (six term test) = -0.5806 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0 y[1] (numeric) = 2.4378339171762955349240414220511 absolute error = 2.4378339171762955349240414220511 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.656 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 = 4.736 Order of pole (six term test) = -0.5818 TOP MAIN SOLVE Loop bytes used=240067824, alloc=4521156, time=18.83 x[1] = 2.6 y[1] (analytic) = 0 y[1] (numeric) = 2.4477687736956872071997136878196 absolute error = 2.4477687736956872071997136878196 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.667 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 = 4.746 Order of pole (six term test) = -0.5829 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0 y[1] (numeric) = 2.4577040821456429322652678854184 absolute error = 2.4577040821456429322652678854184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.678 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 = 4.757 Order of pole (six term test) = -0.5841 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0 y[1] (numeric) = 2.4676398388565790539677536071431 absolute error = 2.4676398388565790539677536071431 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.689 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.767 Order of pole (six term test) = -0.5852 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0 y[1] (numeric) = 2.4775760401936341938344047940514 absolute error = 2.4775760401936341938344047940514 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.777 Order of pole (six term test) = -0.5864 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 0 y[1] (numeric) = 2.4875126825562890701376669763056 absolute error = 2.4875126825562890701376669763056 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.712 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.788 Order of pole (six term test) = -0.5876 TOP MAIN SOLVE Loop bytes used=244068792, alloc=4586680, time=19.15 x[1] = 2.65 y[1] (analytic) = 0 y[1] (numeric) = 2.4974497623779910918982070505369 absolute error = 2.4974497623779910918982070505369 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.723 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.798 Order of pole (six term test) = -0.5888 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0 y[1] (numeric) = 2.5073872761257836596826851576359 absolute error = 2.5073872761257836596826851576359 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.734 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.808 Order of pole (six term test) = -0.59 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0 y[1] (numeric) = 2.5173252202999401061476391581097 absolute error = 2.5173252202999401061476391581097 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.745 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.819 Order of pole (six term test) = -0.5913 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0 y[1] (numeric) = 2.5272635914336022103557903917093 absolute error = 2.5272635914336022103557903917093 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.757 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 = 4.829 Order of pole (six term test) = -0.5925 TOP MAIN SOLVE Loop bytes used=248069772, alloc=4586680, time=19.46 x[1] = 2.69 y[1] (analytic) = 0 y[1] (numeric) = 2.5372023860924232209468136647 absolute error = 2.5372023860924232209468136647 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.768 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 = 4.839 Order of pole (six term test) = -0.5938 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0 y[1] (numeric) = 2.5471416008742153242815050779763 absolute error = 2.5471416008742153242815050779763 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.779 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 = 4.85 Order of pole (six term test) = -0.595 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 0 y[1] (numeric) = 2.5570812324086014946967004741106 absolute error = 2.5570812324086014946967004741106 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.79 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 = 4.86 Order of pole (six term test) = -0.5963 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 0 y[1] (numeric) = 2.5670212773566716650086089550159 absolute error = 2.5670212773566716650086089550159 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.801 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.87 Order of pole (six term test) = -0.5976 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0 y[1] (numeric) = 2.5769617324106431563847862404778 absolute error = 2.5769617324106431563847862404778 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.813 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.881 Order of pole (six term test) = -0.5989 TOP MAIN SOLVE Loop bytes used=252070716, alloc=4586680, time=19.64 x[1] = 2.74 y[1] (analytic) = 0 y[1] (numeric) = 2.5869025942935253076701300462303 absolute error = 2.5869025942935253076701300462303 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.824 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.891 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 0 y[1] (numeric) = 2.596843859758788245200375093197 absolute error = 2.596843859758788245200375093197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.835 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.901 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0 y[1] (numeric) = 2.606785525590035735067932418038 absolute error = 2.606785525590035735067932418038 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.846 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.912 Order of pole (six term test) = -0.6028 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0 y[1] (numeric) = 2.6167275886006820607198827787648 absolute error = 2.6167275886006820607198827787648 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.857 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.922 Order of pole (six term test) = -0.6041 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0 y[1] (numeric) = 2.6266700456336328696668165835754 absolute error = 2.6266700456336328696668165835754 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.869 Order of pole (ratio test) Not computed bytes used=256071724, alloc=4586680, time=19.77 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) = -0.6055 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0 y[1] (numeric) = 2.6366128935609699339643255314998 absolute error = 2.6366128935609699339643255314998 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.88 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 = 4.942 Order of pole (six term test) = -0.6068 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0 y[1] (numeric) = 2.6465561292836397699965999840971 absolute error = 2.6465561292836397699965999840971 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.891 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 = 4.953 Order of pole (six term test) = -0.6082 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 0 y[1] (numeric) = 2.6564997497311460639440704166436 absolute error = 2.6564997497311460639440704166436 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.902 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.963 Order of pole (six term test) = -0.6096 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 0 y[1] (numeric) = 2.6664437518612458501546441888344 absolute error = 2.6664437518612458501546441888344 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.913 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.973 Order of pole (six term test) = -0.611 TOP MAIN SOLVE Loop bytes used=260072496, alloc=4586680, time=19.90 x[1] = 2.83 y[1] (analytic) = 0 y[1] (numeric) = 2.6763881326596493904611171758946 absolute error = 2.6763881326596493904611171758946 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.924 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.984 Order of pole (six term test) = -0.6124 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 0 y[1] (numeric) = 2.6863328891397237032960642849197 absolute error = 2.6863328891397237032960642849197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.936 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.994 Order of pole (six term test) = -0.6138 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0 y[1] (numeric) = 2.6962780183421996922502083891256 absolute error = 2.6962780183421996922502083891256 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.947 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.004 Order of pole (six term test) = -0.6152 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 0 y[1] (numeric) = 2.7062235173348828245012027891654 absolute error = 2.7062235173348828245012027891654 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.958 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.015 Order of pole (six term test) = -0.6166 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0 y[1] (numeric) = 2.7161693832123673103072013375566 absolute error = 2.7161693832123673103072013375566 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.969 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.025 Order of pole (six term test) = -0.6181 TOP MAIN SOLVE Loop bytes used=264073552, alloc=4586680, time=20.04 x[1] = 2.88 y[1] (analytic) = 0 y[1] (numeric) = 2.7261156130957537355137906884326 absolute error = 2.7261156130957537355137906884326 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.035 Order of pole (six term test) = -0.6195 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0 y[1] (numeric) = 2.7360622041323700997640732029708 absolute error = 2.7360622041323700997640732029708 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.991 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.046 Order of pole (six term test) = -0.621 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0 y[1] (numeric) = 2.7460091534954962138301640110533 absolute error = 2.7460091534954962138301640110533 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.003 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.056 Order of pole (six term test) = -0.6224 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 0 y[1] (numeric) = 2.7559564583840914102003436000125 absolute error = 2.7559564583840914102003436000125 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.014 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.066 Order of pole (six term test) = -0.6239 TOP MAIN SOLVE Loop bytes used=268074612, alloc=4586680, time=20.17 x[1] = 2.92 y[1] (analytic) = 0 y[1] (numeric) = 2.7659041160225255217598250252138 absolute error = 2.7659041160225255217598250252138 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.025 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.076 Order of pole (six term test) = -0.6254 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0 y[1] (numeric) = 2.775852123660313084094784438366 absolute error = 2.775852123660313084094784438366 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.036 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.087 Order of pole (six term test) = -0.6269 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 0 y[1] (numeric) = 2.7858004785718507176291923134055 absolute error = 2.7858004785718507176291923134055 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.047 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.097 Order of pole (six term test) = -0.6284 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0 y[1] (numeric) = 2.7957491780561576464722930131759 absolute error = 2.7957491780561576464722930131759 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.058 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.107 Order of pole (six term test) = -0.6299 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0 y[1] (numeric) = 2.8056982194366193115115300769259 absolute error = 2.8056982194366193115115300769259 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.069 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 = 5.118 Order of pole (six term test) = -0.6314 TOP MAIN SOLVE Loop bytes used=272075784, alloc=4586680, time=20.31 x[1] = 2.97 y[1] (analytic) = 0 y[1] (numeric) = 2.8156476000607340359315172140847 absolute error = 2.8156476000607340359315172140847 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.08 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 = 5.128 Order of pole (six term test) = -0.6329 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0 y[1] (numeric) = 2.8255973172998627019745194615161 absolute error = 2.8255973172998627019745194615161 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.092 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.138 Order of pole (six term test) = -0.6345 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 0 y[1] (numeric) = 2.8355473685489813983820399983915 absolute error = 2.8355473685489813983820399983915 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.103 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.149 Order of pole (six term test) = -0.636 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 0 y[1] (numeric) = 2.8454977512264369985707062114743 absolute error = 2.8454977512264369985707062114743 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.114 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.159 Order of pole (six term test) = -0.6376 TOP MAIN SOLVE Loop bytes used=276076728, alloc=4586680, time=20.44 x[1] = 3.01 y[1] (analytic) = 0 y[1] (numeric) = 2.8554484627737056301989101521363 absolute error = 2.8554484627737056301989101521363 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.125 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.169 Order of pole (six term test) = -0.6392 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 0 y[1] (numeric) = 2.8653995006551539973737758963923 absolute error = 2.8653995006551539973737758963923 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.136 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.179 Order of pole (six term test) = -0.6407 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 0 y[1] (numeric) = 2.8753508623578035173311879551498 absolute error = 2.8753508623578035173311879551498 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.147 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.19 Order of pole (six term test) = -0.6423 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 0 y[1] (numeric) = 2.8853025453910972339950053885381 absolute error = 2.8853025453910972339950053885381 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.158 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.2 Order of pole (six term test) = -0.6439 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 0 y[1] (numeric) = 2.8952545472866694713853865059938 absolute error = 2.8952545472866694713853865059938 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.169 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.21 Order of pole (six term test) = -0.6455 TOP MAIN SOLVE Loop bytes used=280077680, alloc=4586680, time=20.58 x[1] = 3.06 y[1] (analytic) = 0 y[1] (numeric) = 2.9052068655981181904005361619187 absolute error = 2.9052068655981181904005361619187 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.221 Order of pole (six term test) = -0.6471 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 0 y[1] (numeric) = 2.9151594979007800130413352743687 absolute error = 2.9151594979007800130413352743687 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.192 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 = 5.231 Order of pole (six term test) = -0.6487 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 0 y[1] (numeric) = 2.9251124417915078786843903798294 absolute error = 2.9251124417915078786843903798294 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.203 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 = 5.241 Order of pole (six term test) = -0.6504 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 0 y[1] (numeric) = 2.9350656948884512975362164357852 absolute error = 2.9350656948884512975362164357852 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.214 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 = 5.251 Order of pole (six term test) = -0.652 TOP MAIN SOLVE Loop bytes used=284078872, alloc=4586680, time=20.71 x[1] = 3.1 y[1] (analytic) = 0 y[1] (numeric) = 2.9450192548308391669197019817496 absolute error = 2.9450192548308391669197019817496 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.225 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 = 5.262 Order of pole (six term test) = -0.6536 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 0 y[1] (numeric) = 2.9549731192787651165538621718471 absolute error = 2.9549731192787651165538621718471 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.236 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 = 5.272 Order of pole (six term test) = -0.6553 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 0 y[1] (numeric) = 2.9649272859129753494893188889352 absolute error = 2.9649272859129753494893188889352 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.247 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 = 5.282 Order of pole (six term test) = -0.6569 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 0 y[1] (numeric) = 2.9748817524346589458551117907616 absolute error = 2.9748817524346589458551117907616 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.258 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 = 5.292 Order of pole (six term test) = -0.6586 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 0 y[1] (numeric) = 2.9848365165652405970574902986151 absolute error = 2.9848365165652405970574902986151 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.269 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 = 5.303 Order of pole (six term test) = -0.6603 TOP MAIN SOLVE Loop bytes used=288079860, alloc=4586680, time=20.84 x[1] = 3.15 y[1] (analytic) = 0 y[1] (numeric) = 2.9947915760461757385484117878977 absolute error = 2.9947915760461757385484117878977 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.28 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 = 5.313 Order of pole (six term test) = -0.6619 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 0 y[1] (numeric) = 3.0047469286387480497507202066455 absolute error = 3.0047469286387480497507202066455 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.291 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 = 5.323 Order of pole (six term test) = -0.6636 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0 y[1] (numeric) = 3.0147025721238692901885437838192 absolute error = 3.0147025721238692901885437838192 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.302 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 = 5.333 Order of pole (six term test) = -0.6653 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0 y[1] (numeric) = 3.0246585043018814413254693310287 absolute error = 3.0246585043018814413254693310287 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.313 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 = 5.344 Order of pole (six term test) = -0.667 TOP MAIN SOLVE Loop bytes used=292080748, alloc=4586680, time=20.98 x[1] = 3.19 y[1] (analytic) = 0 y[1] (numeric) = 3.0346147229923611240596600722681 absolute error = 3.0346147229923611240596600722681 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.324 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 = 5.354 Order of pole (six term test) = -0.6687 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0 y[1] (numeric) = 3.0445712260339262622644174448743 absolute error = 3.0445712260339262622644174448743 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.335 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 = 5.364 Order of pole (six term test) = -0.6704 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 0 y[1] (numeric) = 3.0545280112840449631948757536427 absolute error = 3.0545280112840449631948757536427 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.346 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 = 5.374 Order of pole (six term test) = -0.6722 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0 y[1] (numeric) = 3.0644850766188465860066902016057 absolute error = 3.0644850766188465860066902016057 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.357 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 = 5.385 Order of pole (six term test) = -0.6739 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 0 y[1] (numeric) = 3.0744424199329349700508594139835 absolute error = 3.0744424199329349700508594139835 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.369 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.395 Order of pole (six term test) = -0.6756 TOP MAIN SOLVE Loop bytes used=296081704, alloc=4586680, time=21.11 x[1] = 3.24 y[1] (analytic) = 0 y[1] (numeric) = 3.0844000391392037950203363947351 absolute error = 3.0844000391392037950203363947351 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.405 Order of pole (six term test) = -0.6773 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0 y[1] (numeric) = 3.0943579321686540454289477692199 absolute error = 3.0943579321686540454289477692199 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.391 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.415 Order of pole (six term test) = -0.6791 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0 y[1] (numeric) = 3.104316096970213552301478667346 absolute error = 3.104316096970213552301478667346 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.402 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.426 Order of pole (six term test) = -0.6808 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0 y[1] (numeric) = 3.1142745315105585853457058696693 absolute error = 3.1142745315105585853457058696693 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.413 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.436 Order of pole (six term test) = -0.6826 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 0 y[1] (numeric) = 3.1242332337739374692627887887214 absolute error = 3.1242332337739374692627887887214 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.424 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.446 Order of pole (six term test) = -0.6843 bytes used=300082932, alloc=4586680, time=21.24 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0 y[1] (numeric) = 3.1341922017619961982318681860971 absolute error = 3.1341922017619961982318681860971 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.435 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.456 Order of pole (six term test) = -0.6861 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 0 y[1] (numeric) = 3.1441514334936060229780857584629 absolute error = 3.1441514334936060229780857584629 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.446 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.467 Order of pole (six term test) = -0.6879 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0 y[1] (numeric) = 3.1541109270046929852006312637574 absolute error = 3.1541109270046929852006312637574 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.457 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.477 Order of pole (six term test) = -0.6897 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0 y[1] (numeric) = 3.1640706803480693744989530236102 absolute error = 3.1640706803480693744989530236102 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.468 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.487 Order of pole (six term test) = -0.6914 TOP MAIN SOLVE Loop bytes used=304083712, alloc=4586680, time=21.38 x[1] = 3.33 y[1] (analytic) = 0 y[1] (numeric) = 3.1740306915932670832910357144929 absolute error = 3.1740306915932670832910357144929 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.479 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.497 Order of pole (six term test) = -0.6932 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0 y[1] (numeric) = 3.183990958826372835567757640195 absolute error = 3.183990958826372835567757640195 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.508 Order of pole (six term test) = -0.695 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 0 y[1] (numeric) = 3.1939514801498652656718875024321 absolute error = 3.1939514801498652656718875024321 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.501 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.518 Order of pole (six term test) = -0.6968 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 0 y[1] (numeric) = 3.2039122536824538236293654848623 absolute error = 3.2039122536824538236293654848623 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.512 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.528 Order of pole (six term test) = -0.6986 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0 y[1] (numeric) = 3.2138732775589194838942307982515 absolute error = 3.2138732775589194838942307982515 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.523 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.538 Order of pole (six term test) = -0.7004 TOP MAIN SOLVE Loop bytes used=308084700, alloc=4586680, time=21.51 x[1] = 3.38 y[1] (analytic) = 0 y[1] (numeric) = 3.2238345499299572346970014294017 absolute error = 3.2238345499299572346970014294017 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.534 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.548 Order of pole (six term test) = -0.7022 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 0 y[1] (numeric) = 3.2337960689620203255095736290737 absolute error = 3.2337960689620203255095736290737 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.545 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.559 Order of pole (six term test) = -0.704 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0 y[1] (numeric) = 3.2437578328371662504578788440711 absolute error = 3.2437578328371662504578788440711 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.556 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.569 Order of pole (six term test) = -0.7058 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 0 y[1] (numeric) = 3.2537198397529044458267028062403 absolute error = 3.2537198397529044458267028062403 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.567 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.579 Order of pole (six term test) = -0.7076 TOP MAIN SOLVE Loop bytes used=312085748, alloc=4586680, time=21.64 x[1] = 3.42 y[1] (analytic) = 0 y[1] (numeric) = 3.2636820879220456801093221131513 absolute error = 3.2636820879220456801093221131513 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.578 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.589 Order of pole (six term test) = -0.7094 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0 y[1] (numeric) = 3.2736445755725531153580329997506 absolute error = 3.2736445755725531153580329997506 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.589 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.599 Order of pole (six term test) = -0.7113 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0 y[1] (numeric) = 3.2836073009473950188903186208236 absolute error = 3.2836073009473950188903186208236 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.61 Order of pole (six term test) = -0.7131 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0 y[1] (numeric) = 3.2935702623043991046994069729376 absolute error = 3.2935702623043991046994069729376 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.611 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.62 Order of pole (six term test) = -0.7149 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 0 y[1] (numeric) = 3.3035334579161084842073919652586 absolute error = 3.3035334579161084842073919652586 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.622 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 = 5.63 Order of pole (six term test) = -0.7167 TOP MAIN SOLVE Loop bytes used=316086984, alloc=4586680, time=21.78 x[1] = 3.47 y[1] (analytic) = 0 y[1] (numeric) = 3.3134968860696392062840039680624 absolute error = 3.3134968860696392062840039680624 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.633 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 = 5.64 Order of pole (six term test) = -0.7186 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0 y[1] (numeric) = 3.3234605450665393667346008070632 absolute error = 3.3234605450665393667346008070632 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.644 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 = 5.651 Order of pole (six term test) = -0.7204 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 0 y[1] (numeric) = 3.3334244332226497677370815568574 absolute error = 3.3334244332226497677370815568574 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.654 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.661 Order of pole (six term test) = -0.7222 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 0 y[1] (numeric) = 3.3433885488679661079792781184255 absolute error = 3.3433885488679661079792781184255 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.665 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.671 Order of pole (six term test) = -0.7241 TOP MAIN SOLVE Loop bytes used=320087900, alloc=4586680, time=21.91 x[1] = 3.51 y[1] (analytic) = 0 y[1] (numeric) = 3.3533528903465026845160265480854 absolute error = 3.3533528903465026845160265480854 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.676 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.681 Order of pole (six term test) = -0.7259 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 0 y[1] (numeric) = 3.3633174560161575876286331750861 absolute error = 3.3633174560161575876286331750861 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.687 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.691 Order of pole (six term test) = -0.7277 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0 y[1] (numeric) = 3.3732822442485793702289000987859 absolute error = 3.3732822442485793702289000987859 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.698 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.701 Order of pole (six term test) = -0.7296 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0 y[1] (numeric) = 3.3832472534290351736053297779741 absolute error = 3.3832472534290351736053297779741 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.709 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.712 Order of pole (six term test) = -0.7314 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0 y[1] (numeric) = 3.3932124819562802915606569122368 absolute error = 3.3932124819562802915606569122368 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.722 Order of pole (six term test) = -0.7332 TOP MAIN SOLVE Loop bytes used=324089244, alloc=4586680, time=22.05 x[1] = 3.56 y[1] (analytic) = 0 y[1] (numeric) = 3.403177928242429155237524206165 absolute error = 3.403177928242429155237524206165 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.731 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.732 Order of pole (six term test) = -0.7351 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 0 y[1] (numeric) = 3.4131435907128277211729922049991 absolute error = 3.4131435907128277211729922049991 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.742 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.742 Order of pole (six term test) = -0.7369 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0 y[1] (numeric) = 3.4231094678059272453627162887134 absolute error = 3.4231094678059272453627162887134 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.753 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.752 Order of pole (six term test) = -0.7388 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0 y[1] (numeric) = 3.4330755579731594263520990190868 absolute error = 3.4330755579731594263520990190868 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.764 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.763 Order of pole (six term test) = -0.7406 TOP MAIN SOLVE Loop bytes used=328090212, alloc=4586680, time=22.18 x[1] = 3.6 y[1] (analytic) = 0 y[1] (numeric) = 3.4430418596788129006045950981195 absolute error = 3.4430418596788129006045950981195 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.775 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.773 Order of pole (six term test) = -0.7424 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0 y[1] (numeric) = 3.4530083713999110736266698253509 absolute error = 3.4530083713999110736266698253509 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.786 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.783 Order of pole (six term test) = -0.7443 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 0 y[1] (numeric) = 3.4629750916260912705547496300918 absolute error = 3.4629750916260912705547496300918 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.797 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.793 Order of pole (six term test) = -0.7461 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 0 y[1] (numeric) = 3.4729420188594851901319134033079 absolute error = 3.4729420188594851901319134033079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.808 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.803 Order of pole (six term test) = -0.748 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0 y[1] (numeric) = 3.4829091516146006462211132928329 absolute error = 3.4829091516146006462211132928329 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.819 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.813 Order of pole (six term test) = -0.7498 TOP MAIN SOLVE Loop bytes used=332091280, alloc=4586680, time=22.31 x[1] = 3.65 y[1] (analytic) = 0 y[1] (numeric) = 3.4928764884182045812174396350197 absolute error = 3.4928764884182045812174396350197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.829 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.824 Order of pole (six term test) = -0.7516 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0 y[1] (numeric) = 3.5028440278092073359344120273741 absolute error = 3.5028440278092073359344120273741 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.834 Order of pole (six term test) = -0.7535 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0 y[1] (numeric) = 3.512811768338548160748541443353 absolute error = 3.512811768338548160748541443353 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.851 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.844 Order of pole (six term test) = -0.7553 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 0 y[1] (numeric) = 3.5227797085690819529925200072671 absolute error = 3.5227797085690819529925200072671 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.862 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.854 Order of pole (six term test) = -0.7571 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0 y[1] (numeric) = 3.5327478470754672057904078703187 absolute error = 3.5327478470754672057904078703187 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.873 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.864 Order of pole (six term test) = -0.759 TOP MAIN SOLVE Loop bytes used=336092284, alloc=4586680, time=22.45 x[1] = 3.7 y[1] (analytic) = 0 y[1] (numeric) = 3.542716182444055153728151894906 absolute error = 3.542716182444055153728151894906 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.884 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.874 Order of pole (six term test) = -0.7608 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0 y[1] (numeric) = 3.5526847132727801009497389693544 absolute error = 3.5526847132727801009497389693544 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.895 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.885 Order of pole (six term test) = -0.7626 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0 y[1] (numeric) = 3.5626534381710509174633072326735 absolute error = 3.5626534381710509174633072326735 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.906 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.895 Order of pole (six term test) = -0.7644 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 0 y[1] (numeric) = 3.5726223557596436896326598878362 absolute error = 3.5726223557596436896326598878362 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.917 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.905 Order of pole (six term test) = -0.7662 TOP MAIN SOLVE Loop bytes used=340093088, alloc=4586680, time=22.58 x[1] = 3.74 y[1] (analytic) = 0 y[1] (numeric) = 3.5825914646705955110178963446012 absolute error = 3.5825914646705955110178963446012 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.928 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.915 Order of pole (six term test) = -0.7681 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 0 y[1] (numeric) = 3.5925607635470993999143410215692 absolute error = 3.5925607635470993999143410215692 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.938 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 = 5.925 Order of pole (six term test) = -0.7699 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0 y[1] (numeric) = 3.6025302510434003301216572716764 absolute error = 3.6025302510434003301216572716764 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.949 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 = 5.935 Order of pole (six term test) = -0.7717 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 0 y[1] (numeric) = 3.612499925824692361655027769054 absolute error = 3.612499925824692361655027769054 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.96 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 = 5.945 Order of pole (six term test) = -0.7735 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0 y[1] (numeric) = 3.6224697865670168582876076913005 absolute error = 3.6224697865670168582876076913005 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.971 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 = 5.956 Order of pole (six term test) = -0.7753 TOP MAIN SOLVE Loop bytes used=344093968, alloc=4586680, time=22.71 x[1] = 3.79 y[1] (analytic) = 0 y[1] (numeric) = 3.6324398319571617789881567385103 absolute error = 3.6324398319571617789881567385103 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.982 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 = 5.966 Order of pole (six term test) = -0.7771 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0 y[1] (numeric) = 3.6424100606925620304898732587318 absolute error = 3.6424100606925620304898732587318 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.993 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 = 5.976 Order of pole (six term test) = -0.7789 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0 y[1] (numeric) = 3.652380471481200868396030544951 absolute error = 3.652380471481200868396030544951 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.004 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 = 5.986 Order of pole (six term test) = -0.7807 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0 y[1] (numeric) = 3.6623510630415123343950930283071 absolute error = 3.6623510630415123343950930283071 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.015 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 = 5.996 Order of pole (six term test) = -0.7824 TOP MAIN SOLVE Loop bytes used=348094956, alloc=4586680, time=22.85 x[1] = 3.83 y[1] (analytic) = 0 y[1] (numeric) = 3.6723218341022847173226091786643 absolute error = 3.6723218341022847173226091786643 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.025 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.006 Order of pole (six term test) = -0.7842 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 0 y[1] (numeric) = 3.6822927834025650259693782792635 absolute error = 3.6822927834025650259693782792635 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.036 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.016 Order of pole (six term test) = -0.786 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 0 y[1] (numeric) = 3.6922639096915644616952090029652 absolute error = 3.6922639096915644616952090029652 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.047 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.026 Order of pole (six term test) = -0.7878 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 0 y[1] (numeric) = 3.7022352117285648790650673268652 absolute error = 3.7022352117285648790650673268652 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.058 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.037 Order of pole (six term test) = -0.7895 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0 y[1] (numeric) = 3.7122066882828262228795875436838 absolute error = 3.7122066882828262228795875436838 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.069 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 = 6.047 Order of pole (six term test) = -0.7913 TOP MAIN SOLVE Loop bytes used=352095980, alloc=4586680, time=22.98 x[1] = 3.88 y[1] (analytic) = 0 y[1] (numeric) = 3.722178338133494930124830059849 absolute error = 3.722178338133494930124830059849 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.08 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 = 6.057 Order of pole (six term test) = -0.793 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0 y[1] (numeric) = 3.7321501600695132855168497555791 absolute error = 3.7321501600695132855168497555791 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.067 Order of pole (six term test) = -0.7948 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 0 y[1] (numeric) = 3.7421221528895297194651247244623 absolute error = 3.7421221528895297194651247244623 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.101 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.077 Order of pole (six term test) = -0.7965 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0 y[1] (numeric) = 3.75209431540181003742522238318 absolute error = 3.75209431540181003742522238318 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.112 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.087 Order of pole (six term test) = -0.7982 TOP MAIN SOLVE Loop bytes used=356097088, alloc=4586680, time=23.12 x[1] = 3.92 y[1] (analytic) = 0 y[1] (numeric) = 3.7620666464241495697552828035116 absolute error = 3.7620666464241495697552828035116 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.123 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.097 Order of pole (six term test) = -0.8 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0 y[1] (numeric) = 3.7720391447837862313330116209447 absolute error = 3.7720391447837862313330116209447 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.134 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.107 Order of pole (six term test) = -0.8017 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0 y[1] (numeric) = 3.7820118093173144803299303759696 absolute error = 3.7820118093173144803299303759696 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.145 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.118 Order of pole (six term test) = -0.8034 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 0 y[1] (numeric) = 3.7919846388706001656776634220903 absolute error = 3.7919846388706001656776634220903 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.155 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.128 Order of pole (six term test) = -0.8051 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 0 y[1] (numeric) = 3.8019576322986962528970797942104 absolute error = 3.8019576322986962528970797942104 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.166 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.138 Order of pole (six term test) = -0.8068 TOP MAIN SOLVE Loop bytes used=360098468, alloc=4586680, time=23.25 x[1] = 3.97 y[1] (analytic) = 0 y[1] (numeric) = 3.8119307884657594180951873174597 absolute error = 3.8119307884657594180951873174597 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.177 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.148 Order of pole (six term test) = -0.8085 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0 y[1] (numeric) = 3.8219041062449675000668258450745 absolute error = 3.8219041062449675000668258450745 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.188 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.158 Order of pole (six term test) = -0.8102 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0 y[1] (numeric) = 3.8318775845184378005684574006174 absolute error = 3.8318775845184378005684574006174 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.199 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.168 Order of pole (six term test) = -0.8118 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0 y[1] (numeric) = 3.8418512221771462229597331914004 absolute error = 3.8418512221771462229597331914004 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.178 Order of pole (six term test) = -0.8135 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 0 y[1] (numeric) = 3.8518250181208472395350604640074 absolute error = 3.8518250181208472395350604640074 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.22 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 = 6.188 Order of pole (six term test) = -0.8151 TOP MAIN SOLVE Loop bytes used=364099588, alloc=4586680, time=23.39 x[1] = 4.02 y[1] (analytic) = 0 y[1] (numeric) = 3.8617989712579946779921249873506 absolute error = 3.8617989712579946779921249873506 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.231 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 = 6.198 Order of pole (six term test) = -0.8168 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0 y[1] (numeric) = 3.8717730805056633176072760718993 absolute error = 3.8717730805056633176072760718993 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.242 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 = 6.208 Order of pole (six term test) = -0.8184 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 0 y[1] (numeric) = 3.8817473447894712858088784731681 absolute error = 3.8817473447894712858088784731681 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.253 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 = 6.219 Order of pole (six term test) = -0.8201 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0 y[1] (numeric) = 3.8917217630435032459592068094793 absolute error = 3.8917217630435032459592068094793 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.264 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 = 6.229 Order of pole (six term test) = -0.8217 TOP MAIN SOLVE Loop bytes used=368100432, alloc=4586680, time=23.52 x[1] = 4.06 y[1] (analytic) = 0 y[1] (numeric) = 3.9016963342102343672732303022563 absolute error = 3.9016963342102343672732303022563 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.274 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.239 Order of pole (six term test) = -0.8233 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 0 y[1] (numeric) = 3.9116710572404550679187353119336 absolute error = 3.9116710572404550679187353119336 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.285 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.249 Order of pole (six term test) = -0.8249 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0 y[1] (numeric) = 3.9216459310931965224566864293244 absolute error = 3.9216459310931965224566864293244 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.296 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.259 Order of pole (six term test) = -0.8265 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0 y[1] (numeric) = 3.9316209547356569248935594798218 absolute error = 3.9316209547356569248935594798218 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.307 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.269 Order of pole (six term test) = -0.8281 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0 y[1] (numeric) = 3.9415961271431284987286169567986 absolute error = 3.9415961271431284987286169567986 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.318 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.279 Order of pole (six term test) = -0.8296 TOP MAIN SOLVE Loop bytes used=372101324, alloc=4586680, time=23.66 x[1] = 4.11 y[1] (analytic) = 0 y[1] (numeric) = 3.9515714472989252454887629416168 absolute error = 3.9515714472989252454887629416168 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.328 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.289 Order of pole (six term test) = -0.8312 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 0 y[1] (numeric) = 3.9615469141943114233517348892621 absolute error = 3.9615469141943114233517348892621 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.339 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.299 Order of pole (six term test) = -0.8328 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0 y[1] (numeric) = 3.9715225268284307475649877449733 absolute error = 3.9715225268284307475649877449733 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.309 Order of pole (six term test) = -0.8343 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 0 y[1] (numeric) = 3.9814982842082363044727252858824 absolute error = 3.9814982842082363044727252858824 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.361 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.319 Order of pole (six term test) = -0.8358 TOP MAIN SOLVE Loop bytes used=376102504, alloc=4586680, time=23.79 x[1] = 4.15 y[1] (analytic) = 0 y[1] (numeric) = 3.9914741853484211710671575309832 absolute error = 3.9914741853484211710671575309832 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.371 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 = 6.329 Order of pole (six term test) = -0.8373 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0 y[1] (numeric) = 4.0014502292713497320822343192492 absolute error = 4.0014502292713497320822343192492 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.382 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.34 Order of pole (six term test) = -0.8389 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0 y[1] (numeric) = 4.011426415006989686748846121351 absolute error = 4.011426415006989686748846121351 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.393 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.35 Order of pole (six term test) = -0.8404 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 0 y[1] (numeric) = 4.0214027415928447374298158495147 absolute error = 4.0214027415928447374298158495147 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.404 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.36 Order of pole (six term test) = -0.8418 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0 y[1] (numeric) = 4.031379208073887952450951516318 absolute error = 4.031379208073887952450951516318 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.415 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.37 Order of pole (six term test) = -0.8433 TOP MAIN SOLVE Loop bytes used=380103864, alloc=4586680, time=23.92 x[1] = 4.2 y[1] (analytic) = 0 y[1] (numeric) = 4.0413558135024957955410103564398 absolute error = 4.0413558135024957955410103564398 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.425 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 = 6.38 Order of pole (six term test) = -0.8448 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 0 y[1] (numeric) = 4.0513325569383828143886613981396 absolute error = 4.0513325569383828143886613981396 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.436 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 = 6.39 Order of pole (six term test) = -0.8462 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0 y[1] (numeric) = 4.061309437448536980918446035397 absolute error = 4.061309437448536980918446035397 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.447 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 = 6.4 Order of pole (six term test) = -0.8477 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 0 y[1] (numeric) = 4.0712864541071556759803451446961 absolute error = 4.0712864541071556759803451446961 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.458 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 = 6.41 Order of pole (six term test) = -0.8491 TOP MAIN SOLVE Loop bytes used=384104668, alloc=4586680, time=24.06 x[1] = 4.24 y[1] (analytic) = 0 y[1] (numeric) = 4.0812636059955823112388866118272 absolute error = 4.0812636059955823112388866118272 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.468 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.42 Order of pole (six term test) = -0.8505 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0 y[1] (numeric) = 4.0912408922022435811377883512894 absolute error = 4.0912408922022435811377883512894 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.479 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.43 Order of pole (six term test) = -0.8519 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0 y[1] (numeric) = 4.1012183118225873379049482554605 absolute error = 4.1012183118225873379049482554605 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.44 Order of pole (six term test) = -0.8533 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 0 y[1] (numeric) = 4.1111958639590210826501829241937 absolute error = 4.1111958639590210826501829241937 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.501 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.45 Order of pole (six term test) = -0.8547 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0 y[1] (numeric) = 4.121173547720851065694500105167 absolute error = 4.121173547720851065694500105167 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.511 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.46 Order of pole (six term test) = -0.8561 TOP MAIN SOLVE Loop bytes used=388106256, alloc=4586680, time=24.19 x[1] = 4.29 y[1] (analytic) = 0 y[1] (numeric) = 4.1311513622242219893548838198631 absolute error = 4.1311513622242219893548838198631 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.522 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.47 Order of pole (six term test) = -0.8574 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 0 y[1] (numeric) = 4.1411293065920573064925941551582 absolute error = 4.1411293065920573064925941551582 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.533 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.48 Order of pole (six term test) = -0.8588 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 0 y[1] (numeric) = 4.1511073799540001082158533642643 absolute error = 4.1511073799540001082158533642643 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.544 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.491 Order of pole (six term test) = -0.8601 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0 y[1] (numeric) = 4.1610855814463545942095236490792 absolute error = 4.1610855814463545942095236490792 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.554 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 = 6.501 Order of pole (six term test) = -0.8614 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0 y[1] (numeric) = 4.1710639102120281192449969077482 absolute error = 4.1710639102120281192449969077482 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.565 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 = 6.511 Order of pole (six term test) = -0.8627 TOP MAIN SOLVE Loop bytes used=392107056, alloc=4586680, time=24.32 x[1] = 4.34 y[1] (analytic) = 0 y[1] (numeric) = 4.1810423654004738095030296634867 absolute error = 4.1810423654004738095030296634867 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.576 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 = 6.521 Order of pole (six term test) = -0.864 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0 y[1] (numeric) = 4.191020946167633742420683903703 absolute error = 4.191020946167633742420683903703 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.586 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.531 Order of pole (six term test) = -0.8653 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0 y[1] (numeric) = 4.2009996516758826838508929405762 absolute error = 4.2009996516758826838508929405762 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.597 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.541 Order of pole (six term test) = -0.8665 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0 y[1] (numeric) = 4.2109784810939723763994766768675 absolute error = 4.2109784810939723763994766768675 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.608 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.551 Order of pole (six term test) = -0.8678 TOP MAIN SOLVE Loop bytes used=396108064, alloc=4586680, time=24.46 x[1] = 4.38 y[1] (analytic) = 0 y[1] (numeric) = 4.220957433596976372879698582974 absolute error = 4.220957433596976372879698582974 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.619 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.561 Order of pole (six term test) = -0.869 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 0 y[1] (numeric) = 4.230936508366235408898702764595 absolute error = 4.230936508366235408898702764595 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.629 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 = 6.571 Order of pole (six term test) = -0.8702 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 4.2409157045893033086634089733538 absolute error = 4.2409157045893033086634089733538 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.64 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 = 6.581 Order of pole (six term test) = -0.8714 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 0 y[1] (numeric) = 4.2508950214598934181656912852548 absolute error = 4.2508950214598934181656912852548 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.651 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.591 Order of pole (six term test) = -0.8726 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0 y[1] (numeric) = 4.2608744581778255599779371997578 absolute error = 4.2608744581778255599779371997578 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.661 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 = 6.601 Order of pole (six term test) = -0.8738 TOP MAIN SOLVE Loop bytes used=400109048, alloc=4586680, time=24.60 x[1] = 4.43 y[1] (analytic) = 0 y[1] (numeric) = 4.2708540139489735039603926115089 absolute error = 4.2708540139489735039603926115089 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.672 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 = 6.611 Order of pole (six term test) = -0.875 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0 y[1] (numeric) = 4.2808336879852129482510587577599 absolute error = 4.2808336879852129482510587577599 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.683 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 = 6.621 Order of pole (six term test) = -0.8761 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 0 y[1] (numeric) = 4.2908134795043700049773338961908 absolute error = 4.2908134795043700049773338961908 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.693 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.631 Order of pole (six term test) = -0.8773 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0 y[1] (numeric) = 4.3007933877301701851960989418007 absolute error = 4.3007933877301701851960989418007 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.704 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.641 Order of pole (six term test) = -0.8784 TOP MAIN SOLVE Loop bytes used=404109916, alloc=4586680, time=24.73 x[1] = 4.47 y[1] (analytic) = 0 y[1] (numeric) = 4.3107734118921878776355461859611 absolute error = 4.3107734118921878776355461859611 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.651 Order of pole (six term test) = -0.8795 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 0 y[1] (numeric) = 4.3207535512257963158777569143873 absolute error = 4.3207535512257963158777569143873 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.726 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.661 Order of pole (six term test) = -0.8806 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0 y[1] (numeric) = 4.3307338049721180286858603968326 absolute error = 4.3307338049721180286858603968326 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.736 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.671 Order of pole (six term test) = -0.8816 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 4.340714172377975768243566291059 absolute error = 4.340714172377975768243566291059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.747 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.681 Order of pole (six term test) = -0.8827 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 0 y[1] (numeric) = 4.3506946526958439111379677302719 absolute error = 4.3506946526958439111379677302719 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.758 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.692 Order of pole (six term test) = -0.8838 TOP MAIN SOLVE Loop bytes used=408110700, alloc=4586680, time=24.87 x[1] = 4.52 y[1] (analytic) = 0 y[1] (numeric) = 4.360675245183800326978775785411 absolute error = 4.360675245183800326978775785411 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.768 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 = 6.702 Order of pole (six term test) = -0.8848 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 0 y[1] (numeric) = 4.3706559491054787096085799492046 absolute error = 4.3706559491054787096085799492046 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.779 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 = 6.712 Order of pole (six term test) = -0.8858 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0 y[1] (numeric) = 4.3806367637300213659193459180303 absolute error = 4.3806367637300213659193459180303 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.79 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 = 6.722 Order of pole (six term test) = -0.8868 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 0 y[1] (numeric) = 4.3906176883320324573501731966669 absolute error = 4.3906176883320324573501731966669 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.732 Order of pole (six term test) = -0.8878 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 0 y[1] (numeric) = 4.400598722191531689200352675622 absolute error = 4.400598722191531689200352675622 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.811 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.742 Order of pole (six term test) = -0.8888 bytes used=412111804, alloc=4586680, time=25.00 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 0 y[1] (numeric) = 4.4105798645939084429499998991768 absolute error = 4.4105798645939084429499998991768 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.822 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.752 Order of pole (six term test) = -0.8897 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 0 y[1] (numeric) = 4.4205611148298763468380046388126 absolute error = 4.4205611148298763468380046388126 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.832 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.762 Order of pole (six term test) = -0.8907 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 0 y[1] (numeric) = 4.4305424721954282800037428145447 absolute error = 4.4305424721954282800037428145447 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.843 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.772 Order of pole (six term test) = -0.8916 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 4.4405239359917918055549537913825 absolute error = 4.4405239359917918055549537913825 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.854 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.782 Order of pole (six term test) = -0.8925 TOP MAIN SOLVE Loop bytes used=416112884, alloc=4586680, time=25.14 x[1] = 4.61 y[1] (analytic) = 0 y[1] (numeric) = 4.4505055055253850279794054703944 absolute error = 4.4505055055253850279794054703944 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.864 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.792 Order of pole (six term test) = -0.8934 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 0 y[1] (numeric) = 4.4604871801077728703724620727035 absolute error = 4.4604871801077728703724620727035 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.875 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.802 Order of pole (six term test) = -0.8943 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 0 y[1] (numeric) = 4.4704689590556237670064455904091 absolute error = 4.4704689590556237670064455904091 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.886 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.812 Order of pole (six term test) = -0.8951 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 0 y[1] (numeric) = 4.4804508416906667668207518952674 absolute error = 4.4804508416906667668207518952674 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.896 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 = 6.822 Order of pole (six term test) = -0.896 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 0 y[1] (numeric) = 4.4904328273396490434640566352799 absolute error = 4.4904328273396490434640566352799 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.907 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 = 6.832 Order of pole (six term test) = -0.8968 TOP MAIN SOLVE Loop bytes used=420113884, alloc=4586680, time=25.27 x[1] = 4.66 y[1] (analytic) = 0 y[1] (numeric) = 4.5004149153342938075716343321847 absolute error = 4.5004149153342938075716343321847 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.918 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 = 6.842 Order of pole (six term test) = -0.8976 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 0 y[1] (numeric) = 4.5103971050112586170118263827609 absolute error = 4.5103971050112586170118263827609 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.928 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.852 Order of pole (six term test) = -0.8984 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 0 y[1] (numeric) = 4.5203793957120940808860396725444 absolute error = 4.5203793957120940808860396725444 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.939 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.862 Order of pole (six term test) = -0.8992 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 0 y[1] (numeric) = 4.5303617867832029531163467885412 absolute error = 4.5303617867832029531163467885412 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.872 Order of pole (six term test) = -0.9 TOP MAIN SOLVE Loop bytes used=424114828, alloc=4586680, time=25.41 x[1] = 4.7 y[1] (analytic) = 0 y[1] (numeric) = 4.5403442775757996115038007747157 absolute error = 4.5403442775757996115038007747157 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.96 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 = 6.882 Order of pole (six term test) = -0.9007 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 0 y[1] (numeric) = 4.5503268674458699181889812702954 absolute error = 4.5503268674458699181889812702954 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.971 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 = 6.892 Order of pole (six term test) = -0.9014 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 0 y[1] (numeric) = 4.5603095557541314574940638215514 absolute error = 4.5603095557541314574940638215514 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.981 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.902 Order of pole (six term test) = -0.9022 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 0 y[1] (numeric) = 4.5702923418659941471728591358653 absolute error = 4.5702923418659941471728591358653 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.992 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.912 Order of pole (six term test) = -0.9029 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 0 y[1] (numeric) = 4.5802752251515212191418128860443 absolute error = 4.5802752251515212191418128860443 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.003 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.922 Order of pole (six term test) = -0.9036 TOP MAIN SOLVE Loop bytes used=428115744, alloc=4586680, time=25.54 x[1] = 4.75 y[1] (analytic) = 0 y[1] (numeric) = 4.5902582049853905658108980691059 absolute error = 4.5902582049853905658108980691059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.013 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.932 Order of pole (six term test) = -0.9042 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 0 y[1] (numeric) = 4.6002412807468564481786794382094 absolute error = 4.6002412807468564481786794382094 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.024 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.942 Order of pole (six term test) = -0.9049 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 0 y[1] (numeric) = 4.6102244518197115619005915873805 absolute error = 4.6102244518197115619005915873805 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.035 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.952 Order of pole (six term test) = -0.9055 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 0 y[1] (numeric) = 4.6202077175922494575836571739625 absolute error = 4.6202077175922494575836571739625 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.045 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.963 Order of pole (six term test) = -0.9062 TOP MAIN SOLVE Loop bytes used=432116684, alloc=4586680, time=25.68 x[1] = 4.79 y[1] (analytic) = 0 y[1] (numeric) = 4.6301910774572273116044876827995 absolute error = 4.6301910774572273116044876827995 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.056 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.973 Order of pole (six term test) = -0.9068 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 0 y[1] (numeric) = 4.6401745308118290437904641123082 absolute error = 4.6401745308118290437904641123082 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.066 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.983 Order of pole (six term test) = -0.9074 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 0 y[1] (numeric) = 4.6501580770576287783464969150546 absolute error = 4.6501580770576287783464969150546 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.077 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.993 Order of pole (six term test) = -0.9079 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 0 y[1] (numeric) = 4.6601417156005546444517212514655 absolute error = 4.6601417156005546444517212514655 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.088 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.003 Order of pole (six term test) = -0.9085 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 0 y[1] (numeric) = 4.6701254458508529129919027921701 absolute error = 4.6701254458508529129919027921701 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.098 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.013 Order of pole (six term test) = -0.909 TOP MAIN SOLVE Loop bytes used=436117688, alloc=4586680, time=25.81 x[1] = 4.84 y[1] (analytic) = 0 y[1] (numeric) = 4.6801092672230524659342184915356 absolute error = 4.6801092672230524659342184915356 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.109 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.023 Order of pole (six term test) = -0.9096 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 0 y[1] (numeric) = 4.690093179135929594891443395609 absolute error = 4.690093179135929594891443395609 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.033 Order of pole (six term test) = -0.9101 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 0 y[1] (numeric) = 4.7000771810124731254624259712222 absolute error = 4.7000771810124731254624259712222 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.13 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 = 7.043 Order of pole (six term test) = -0.9106 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 0 y[1] (numeric) = 4.7100612722798498639750778666437 absolute error = 4.7100612722798498639750778666437 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.141 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 = 7.053 Order of pole (six term test) = -0.9111 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 0 y[1] (numeric) = 4.7200454523693703632969465447332 absolute error = 4.7200454523693703632969465447332 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.151 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 = 7.063 Order of pole (six term test) = -0.9115 TOP MAIN SOLVE Loop bytes used=440118728, alloc=4586680, time=25.95 x[1] = 4.89 y[1] (analytic) = 0 y[1] (numeric) = 4.7300297207164550044167878655094 absolute error = 4.7300297207164550044167878655094 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.162 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 = 7.073 Order of pole (six term test) = -0.912 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 0 y[1] (numeric) = 4.7400140767606003905384173281138 absolute error = 4.7400140767606003905384173281138 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.173 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 = 7.083 Order of pole (six term test) = -0.9124 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 0 y[1] (numeric) = 4.7499985199453460504655000992056 absolute error = 4.7499985199453460504655000992056 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.183 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.093 Order of pole (six term test) = -0.9128 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 0 y[1] (numeric) = 4.7599830497182414480928478395239 absolute error = 4.7599830497182414480928478395239 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.194 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.103 Order of pole (six term test) = -0.9132 TOP MAIN SOLVE Loop bytes used=444119468, alloc=4586680, time=26.08 x[1] = 4.93 y[1] (analytic) = 0 y[1] (numeric) = 4.7699676655308132948562312749177 absolute error = 4.7699676655308132948562312749177 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.204 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.113 Order of pole (six term test) = -0.9136 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 0 y[1] (numeric) = 4.7799523668385331620286979249781 absolute error = 4.7799523668385331620286979249781 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.215 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.123 Order of pole (six term test) = -0.914 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 0 y[1] (numeric) = 4.7899371531007853897869107857688 absolute error = 4.7899371531007853897869107857688 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.225 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 = 7.133 Order of pole (six term test) = -0.9143 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 0 y[1] (numeric) = 4.7999220237808352900061023507423 absolute error = 4.7999220237808352900061023507423 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.236 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 = 7.143 Order of pole (six term test) = -0.9147 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 0 y[1] (numeric) = 4.8099069783457976397768753385038 absolute error = 4.8099069783457976397768753385038 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.247 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 = 7.153 Order of pole (six term test) = -0.915 TOP MAIN SOLVE Loop bytes used=448120724, alloc=4586680, time=26.22 x[1] = 4.98 y[1] (analytic) = 0 y[1] (numeric) = 4.8198920162666054626712829769806 absolute error = 4.8198920162666054626712829769806 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.257 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.163 Order of pole (six term test) = -0.9153 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 0 y[1] (numeric) = 4.829877137017979094819393678236 absolute error = 4.829877137017979094819393678236 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.268 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.173 Order of pole (six term test) = -0.9156 Finished! diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0)); Iterations = 490 Total Elapsed Time = 26 Seconds Elapsed Time(since restart) = 25 Seconds Time to Timeout = 2 Minutes 33 Seconds Percent Done = 100.2 % > quit bytes used=449711448, alloc=4586680, time=26.27