|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp2[1] := sin(array_tmp1[1]); > array_tmp2_g[1] := cos(array_tmp1[1]); > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D2[1] * array_x[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp4[1] := sin(array_tmp3[1]); > array_tmp4_g[1] := cos(array_tmp3[1]); > #emit pre expt FULL - FULL $eq_no = 1 i = 1 > array_tmp5[1] := expt(array_tmp2[1] , array_tmp4[1] ) ; > array_tmp5_a1[1] := ln(array_tmp2[1] ) ; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp2[2] := array_tmp2_g[1] * array_tmp1[2] / 1; > array_tmp2_g[2] := -array_tmp2[1] * array_tmp1[2] / 1; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := array_const_0D2[1] * array_x[2]; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp4[2] := array_tmp4_g[1] * array_tmp3[2] / 1; > array_tmp4_g[2] := -array_tmp4[1] * array_tmp3[2] / 1; > #emit pre expt FULL - FULL $eq_no = 1 i = 2 > array_tmp5_a1[2] := (array_tmp2[2] -att(1,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1]; > array_tmp5_a2[1] := ats(2,array_tmp2,array_tmp5_a1,1) * 1 / glob_h; > array_tmp5[2] := ats(1,array_tmp5,array_tmp5_a2,1)*glob_h/1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp2[3] := array_tmp2_g[2] * array_tmp1[2] / 2; > array_tmp2_g[3] := -array_tmp2[2] * array_tmp1[2] / 2; > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp4[3] := array_tmp4_g[2] * array_tmp3[2] / 2; > array_tmp4_g[3] := -array_tmp4[2] * array_tmp3[2] / 2; > #emit pre expt FULL - FULL $eq_no = 1 i = 3 > array_tmp5_a1[3] := (array_tmp2[3] -att(2,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1]; > array_tmp5_a2[2] := ats(3,array_tmp2,array_tmp5_a1,1) * 2 / glob_h; > array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h/2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp6[3] := array_tmp5[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp2[4] := array_tmp2_g[3] * array_tmp1[2] / 3; > array_tmp2_g[4] := -array_tmp2[3] * array_tmp1[2] / 3; > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp4[4] := array_tmp4_g[3] * array_tmp3[2] / 3; > array_tmp4_g[4] := -array_tmp4[3] * array_tmp3[2] / 3; > #emit pre expt FULL - FULL $eq_no = 1 i = 4 > array_tmp5_a1[4] := (array_tmp2[4] -att(3,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1]; > array_tmp5_a2[3] := ats(4,array_tmp2,array_tmp5_a1,1) * 3 / glob_h; > array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h/3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp6[4] := array_tmp5[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp2[5] := array_tmp2_g[4] * array_tmp1[2] / 4; > array_tmp2_g[5] := -array_tmp2[4] * array_tmp1[2] / 4; > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp4[5] := array_tmp4_g[4] * array_tmp3[2] / 4; > array_tmp4_g[5] := -array_tmp4[4] * array_tmp3[2] / 4; > #emit pre expt FULL - FULL $eq_no = 1 i = 5 > array_tmp5_a1[5] := (array_tmp2[5] -att(4,array_tmp2,array_tmp5_a1,2))/ array_tmp2[1]; > array_tmp5_a2[4] := ats(5,array_tmp2,array_tmp5_a1,1) * 4 / glob_h; > array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h/4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp6[5] := array_tmp5[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp6[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp2[kkk] := array_tmp2_g[kkk - 1] * array_tmp1[2] / (kkk - 1); > array_tmp2_g[kkk] := -array_tmp2[kkk - 1] * array_tmp1[2] / (kkk - 1); > #emit sin LINEAR $eq_no = 1 > array_tmp4[kkk] := array_tmp4_g[kkk - 1] * array_tmp3[2] / (kkk - 1); > array_tmp4_g[kkk] := -array_tmp4[kkk - 1] * array_tmp3[2] / (kkk - 1); > #emit expt FULL FULL $eq_no = 1 i = 1 > array_tmp5_a1[kkk] := (array_tmp2[kkk] - att(kkk-1,array_tmp2,array_tmp5_a1,2))/array_tmp2[1]; > array_tmp5_a2[kkk-1] := ats(kkk,array_tmp2,array_tmp5_a1,1) * (kkk-1)/glob_h; > array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1) * glob_h/(kkk-1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp6[kkk] := array_tmp5[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp6[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_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_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := sin(array_tmp1[1]); array_tmp2_g[1] := cos(array_tmp1[1]); array_tmp3[1] := array_const_0D2[1]*array_x[1]; array_tmp4[1] := sin(array_tmp3[1]); array_tmp4_g[1] := cos(array_tmp3[1]); array_tmp5[1] := expt(array_tmp2[1], array_tmp4[1]); array_tmp5_a1[1] := ln(array_tmp2[1]); array_tmp6[1] := array_const_0D0[1] + array_tmp5[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp6[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp2_g[1]*array_tmp1[2]; array_tmp2_g[2] := -array_tmp2[1]*array_tmp1[2]; array_tmp3[2] := array_const_0D2[1]*array_x[2]; array_tmp4[2] := array_tmp4_g[1]*array_tmp3[2]; array_tmp4_g[2] := -array_tmp4[1]*array_tmp3[2]; array_tmp5_a1[2] := ( array_tmp2[2] - att(1, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1] ; array_tmp5_a2[1] := ats(2, array_tmp2, array_tmp5_a1, 1)/glob_h; array_tmp5[2] := ats(1, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[2] := array_tmp5[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp6[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp2[3] := 1/2*array_tmp2_g[2]*array_tmp1[2]; array_tmp2_g[3] := -1/2*array_tmp2[2]*array_tmp1[2]; array_tmp4[3] := 1/2*array_tmp4_g[2]*array_tmp3[2]; array_tmp4_g[3] := -1/2*array_tmp4[2]*array_tmp3[2]; array_tmp5_a1[3] := ( array_tmp2[3] - att(2, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1] ; array_tmp5_a2[2] := 2*ats(3, array_tmp2, array_tmp5_a1, 1)/glob_h; array_tmp5[3] := 1/2*ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[3] := array_tmp5[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp6[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp2[4] := 1/3*array_tmp2_g[3]*array_tmp1[2]; array_tmp2_g[4] := -1/3*array_tmp2[3]*array_tmp1[2]; array_tmp4[4] := 1/3*array_tmp4_g[3]*array_tmp3[2]; array_tmp4_g[4] := -1/3*array_tmp4[3]*array_tmp3[2]; array_tmp5_a1[4] := ( array_tmp2[4] - att(3, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1] ; array_tmp5_a2[3] := 3*ats(4, array_tmp2, array_tmp5_a1, 1)/glob_h; array_tmp5[4] := 1/3*ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[4] := array_tmp5[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp6[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp2[5] := 1/4*array_tmp2_g[4]*array_tmp1[2]; array_tmp2_g[5] := -1/4*array_tmp2[4]*array_tmp1[2]; array_tmp4[5] := 1/4*array_tmp4_g[4]*array_tmp3[2]; array_tmp4_g[5] := -1/4*array_tmp4[4]*array_tmp3[2]; array_tmp5_a1[5] := ( array_tmp2[5] - att(4, array_tmp2, array_tmp5_a1, 2))/array_tmp2[1] ; array_tmp5_a2[4] := 4*ats(5, array_tmp2, array_tmp5_a1, 1)/glob_h; array_tmp5[5] := 1/4*ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h; array_tmp6[5] := array_tmp5[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp6[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp2[kkk] := array_tmp2_g[kkk - 1]*array_tmp1[2]/(kkk - 1); array_tmp2_g[kkk] := -array_tmp2[kkk - 1]*array_tmp1[2]/(kkk - 1); array_tmp4[kkk] := array_tmp4_g[kkk - 1]*array_tmp3[2]/(kkk - 1); array_tmp4_g[kkk] := -array_tmp4[kkk - 1]*array_tmp3[2]/(kkk - 1); array_tmp5_a1[kkk] := ( array_tmp2[kkk] - att(kkk - 1, array_tmp2, array_tmp5_a1, 2))/ array_tmp2[1]; array_tmp5_a2[kkk - 1] := ats(kkk, array_tmp2, array_tmp5_a1, 1)*(kkk - 1)/glob_h; array_tmp5[kkk] := ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/(kkk - 1); array_tmp6[kkk] := array_tmp5[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp6[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(0.0); > end; exact_soln_y := proc(x) return 0. end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #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_g, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5_c1, > array_tmp5_a1, > array_tmp5_a2, > array_tmp5, > array_tmp6, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/expt_sin_sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"); > 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_g:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_g:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5_c1:= Array(0..(max_terms + 1),[]); > array_tmp5_a1:= Array(0..(max_terms + 1),[]); > array_tmp5_a2:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T02:11:56-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_sin_sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"expt_sin_sin diffeq.mxt") > ; > logitem_str(html_log_file,"expt_sin_sin maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2_g, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5_c1, array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/expt_sin_sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"); 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_g := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_g := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5_c1 := Array(0 .. max_terms + 1, []); array_tmp5_a1 := Array(0 .. max_terms + 1, []); array_tmp5_a2 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_c1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_g[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_c1[term] := 0.; term := term + 1 end do; array_tmp5_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_a1[term] := 0.; term := term + 1 end do; array_tmp5_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_a2[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T02:11:56-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_sin_sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x));") ; logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "expt_sin_sin diffeq.mxt"); logitem_str(html_log_file, "expt_sin_sin maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/expt_sin_sinpostode.ode################# diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x)); ! #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 = 6.1580667061193463283102985920761e-138 estimated_step_error = 6.1580667061193463283102985920761e-138 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 = 4.1325902477166683471631527296199e-130 estimated_step_error = 4.1325902477166683471631527296199e-130 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7733097227820050397534685526695e-122 estimated_step_error = 2.7733097227820050397534685526695e-122 best_h = 8.000e-06 opt_iter = 4 bytes used=4000340, alloc=2883056, time=0.12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.8611035714292238514002739779852e-114 estimated_step_error = 1.8611035714292238514002739779852e-114 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 = 1.2489210695060421828826037642302e-106 estimated_step_error = 1.2489210695060421828826037642302e-106 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 = 8.3807716223282562456921229872124e-99 estimated_step_error = 8.3807716223282562456921229872124e-99 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 = 5.6234411354117810322076598231255e-91 estimated_step_error = 5.6234411354117810322076598231255e-91 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.7727548599635948747414676343202e-83 estimated_step_error = 3.7727548599635948747414676343202e-83 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 = 2.5304145384643581736578338334024e-75 estimated_step_error = 2.5304145384643581736578338334024e-75 best_h = 0.000512 opt_iter = 10 bytes used=8001560, alloc=3931440, time=0.24 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6962051920553500734982660050491e-67 estimated_step_error = 1.6962051920553500734982660050491e-67 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 = 1.1357262095253179750615022907652e-59 estimated_step_error = 1.1357262095253179750615022907652e-59 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.5873694205637514136430654108408e-52 estimated_step_error = 7.5873694205637514136430654108408e-52 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 = 5.0463211439842927898294863206237e-44 estimated_step_error = 5.0463211439842927898294863206237e-44 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 = 3.3272125955593747257439418741568e-36 estimated_step_error = 3.3272125955593747257439418741568e-36 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 = 2.1578615880663676758797205621482e-28 estimated_step_error = 2.1578615880663676758797205621482e-28 best_h = 0.032768 opt_iter = 16 bytes used=12002728, alloc=4062488, time=0.37 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3598638714045118010169601950896e-20 estimated_step_error = 1.3598638714045118010169601950896e-20 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.2742829905347028653944741323172e-13 estimated_step_error = 8.2742829905347028653944741323172e-13 best_h = 0.032768 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 = 0.115 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0 y[1] (numeric) = 0.009103889960356604130910550086889 absolute error = 0.009103889960356604130910550086889 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1265 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0 y[1] (numeric) = 0.018143682483077007537188336820091 absolute error = 0.018143682483077007537188336820091 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.138 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0 y[1] (numeric) = 0.027121430896624074502472278849572 absolute error = 0.027121430896624074502472278849572 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1496 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=16003416, alloc=4193536, time=0.50 x[1] = 0.14 y[1] (analytic) = 0 y[1] (numeric) = 0.036039022352262450542773560612856 absolute error = 0.036039022352262450542773560612856 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1611 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0 y[1] (numeric) = 0.044898202154845721031850816708976 absolute error = 0.044898202154845721031850816708976 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1726 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0 y[1] (numeric) = 0.053700593046732205430679694442642 absolute error = 0.053700593046732205430679694442642 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1841 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0 y[1] (numeric) = 0.062447710760794217789837427677364 absolute error = 0.062447710760794217789837427677364 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.1956 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0 y[1] (numeric) = 0.071140976754020186177791182350021 absolute error = 0.071140976754020186177791182350021 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2071 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0 y[1] (numeric) = 0.079781728769672483805822843116674 absolute error = 0.079781728769672483805822843116674 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2186 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20004284, alloc=4259060, time=0.63 x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.088371229699107955686798823658397 absolute error = 0.088371229699107955686798823658397 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2301 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0 y[1] (numeric) = 0.096910675092598238792198404348142 absolute error = 0.096910675092598238792198404348142 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2416 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0 y[1] (numeric) = 0.10540119958273613176490778804033 absolute error = 0.10540119958273613176490778804033 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2531 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0 y[1] (numeric) = 0.11384388242241290434015090147834 absolute error = 0.11384388242241290434015090147834 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2647 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0 y[1] (numeric) = 0.12223975229430537895179343333101 absolute error = 0.12223975229430537895179343333101 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2762 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=24005392, alloc=4259060, time=0.76 x[1] = 0.25 y[1] (analytic) = 0 y[1] (numeric) = 0.13058979151534242142508029162734 absolute error = 0.13058979151534242142508029162734 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2877 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0 y[1] (numeric) = 0.13889493973439260769108325135319 absolute error = 0.13889493973439260769108325135319 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.2992 Order of pole (ratio test) Not computed 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) = 0.14715609720214923506259618262905 absolute error = 0.14715609720214923506259618262905 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3107 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0 y[1] (numeric) = 0.15537412767730042518177728338078 absolute error = 0.15537412767730042518177728338078 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3222 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0 y[1] (numeric) = 0.16354986102144042274413678789564 absolute error = 0.16354986102144042274413678789564 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3337 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.17168409552599961321209932293773 absolute error = 0.17168409552599961321209932293773 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3452 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=28006356, alloc=4324584, time=0.89 x[1] = 0.31 y[1] (analytic) = 0 y[1] (numeric) = 0.17977760000716085397318222838427 absolute error = 0.17977760000716085397318222838427 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3568 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0 y[1] (numeric) = 0.18783111569885815582976399311572 absolute error = 0.18783111569885815582976399311572 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0 y[1] (numeric) = 0.19584535796920008985118304736261 absolute error = 0.19584535796920008985118304736261 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3798 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0 y[1] (numeric) = 0.20382101788178327154406955493598 absolute error = 0.20382101788178327154406955493598 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.3913 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0 y[1] (numeric) = 0.21175876362017745585522822210634 absolute error = 0.21175876362017745585522822210634 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4028 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0 y[1] (numeric) = 0.21965924179123239512420058060198 absolute error = 0.21965924179123239512420058060198 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4143 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32007320, alloc=4324584, time=1.02 x[1] = 0.37 y[1] (analytic) = 0 y[1] (numeric) = 0.22752307862066870374179864535039 absolute error = 0.22752307862066870374179864535039 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4259 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0 y[1] (numeric) = 0.23535088105258550591401088175142 absolute error = 0.23535088105258550591401088175142 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4374 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0 y[1] (numeric) = 0.2431432377629797537844416438037 absolute error = 0.2431432377629797537844416438037 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4489 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.25090072009607283907993768055703 absolute error = 0.25090072009607283907993768055703 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4604 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0 y[1] (numeric) = 0.25862388293113726179477267919728 absolute error = 0.25862388293113726179477267919728 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4719 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=36009516, alloc=4324584, time=1.15 x[1] = 0.42 y[1] (analytic) = 0 y[1] (numeric) = 0.26631326548657578618557369109174 absolute error = 0.26631326548657578618557369109174 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.4834 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0 y[1] (numeric) = 0.27396939206720035976464203026887 absolute error = 0.27396939206720035976464203026887 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.495 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0 y[1] (numeric) = 0.28159277275996589286587063556963 absolute error = 0.28159277275996589286587063556963 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5065 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0 y[1] (numeric) = 0.28918390408281667244007952247587 absolute error = 0.28918390408281667244007952247587 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.518 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0 y[1] (numeric) = 0.29674326959078584596376514781818 absolute error = 0.29674326959078584596376514781818 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5295 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0 y[1] (numeric) = 0.30427134044303880198242511779169 absolute error = 0.30427134044303880198242511779169 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.541 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=40010536, alloc=4324584, time=1.28 x[1] = 0.48 y[1] (analytic) = 0 y[1] (numeric) = 0.31176857593415924020405668584094 absolute error = 0.31176857593415924020405668584094 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5526 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0 y[1] (numeric) = 0.31923542399263381989004213827636 absolute error = 0.31923542399263381989004213827636 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5641 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.3266723216491904441094908750815 absolute error = 0.3266723216491904441094908750815 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5756 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0 y[1] (numeric) = 0.3340796954773805601564298057221 absolute error = 0.3340796954773805601564298057221 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5871 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0 y[1] (numeric) = 0.34145796200856234890356080336719 absolute error = 0.34145796200856234890356080336719 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.5986 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0 y[1] (numeric) = 0.34880752812323512564894365205098 absolute error = 0.34880752812323512564894365205098 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=44011828, alloc=4324584, time=1.41 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6102 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.058 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0 y[1] (numeric) = 0.35612879142049210932529851881255 absolute error = 0.35612879142049210932529851881255 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6217 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.08784 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0 y[1] (numeric) = 0.36342214056719589525663391448484 absolute error = 0.36342214056719589525663391448484 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6332 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.111 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0 y[1] (numeric) = 0.37068795562833589297210366463059 absolute error = 0.37068795562833589297210366463059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6447 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.131 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0 y[1] (numeric) = 0.37792660837989744154789850808316 absolute error = 0.37792660837989744154789850808316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6563 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1492 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0 y[1] (numeric) = 0.38513846260545638058251261058234 absolute error = 0.38513846260545638058251261058234 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6678 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1661 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop bytes used=48012780, alloc=4324584, time=1.54 x[1] = 0.59 y[1] (analytic) = 0 y[1] (numeric) = 0.39232387437760888974813567593589 absolute error = 0.39232387437760888974813567593589 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6793 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1822 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.39948319232525299235106029681332 absolute error = 0.39948319232525299235106029681332 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6908 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1976 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0 y[1] (numeric) = 0.40661675788765401708395456774917 absolute error = 0.40661675788765401708395456774917 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7024 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2126 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0 y[1] (numeric) = 0.41372490555615045773403458679173 absolute error = 0.41372490555615045773403458679173 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7139 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2271 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0 y[1] (numeric) = 0.42080796310428813194128640662227 absolute error = 0.42080796310428813194128640662227 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7254 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2413 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0 y[1] (numeric) = 0.4278662518071085045964764255363 absolute error = 0.4278662518071085045964764255363 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7369 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2553 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop bytes used=52014552, alloc=4390108, time=1.67 x[1] = 0.65 y[1] (analytic) = 0 y[1] (numeric) = 0.43490008665026079831580981144084 absolute error = 0.43490008665026079831580981144084 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7485 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.269 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0 y[1] (numeric) = 0.44190977652955643944106462790267 absolute error = 0.44190977652955643944106462790267 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2826 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0 y[1] (numeric) = 0.44889562444153793564241911055013 absolute error = 0.44889562444153793564241911055013 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.296 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0 y[1] (numeric) = 0.45585792766559196834449341664232 absolute error = 0.45585792766559196834449341664232 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.783 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3093 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0 y[1] (numeric) = 0.46279697793809788451365359475617 absolute error = 0.46279697793809788451365359475617 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7946 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3224 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop bytes used=56015700, alloc=4390108, time=1.80 x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.46971306161906751183438934186977 absolute error = 0.46971306161906751183438934186977 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8061 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3355 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0 y[1] (numeric) = 0.47660645985169996594354556379573 absolute error = 0.47660645985169996594354556379573 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8176 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3485 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0 y[1] (numeric) = 0.48347744871524557268418437457104 absolute error = 0.48347744871524557268418437457104 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8291 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3615 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0 y[1] (numeric) = 0.49032629937154592961019448897598 absolute error = 0.49032629937154592961019448897598 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8407 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3744 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0 y[1] (numeric) = 0.49715327820559224531349281902956 absolute error = 0.49715327820559224531349281902956 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8522 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3872 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0 y[1] (numeric) = 0.50395864696042121392002294853202 absolute error = 0.50395864696042121392002294853202 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8637 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop bytes used=60017860, alloc=4390108, time=1.93 x[1] = 0.76 y[1] (analytic) = 0 y[1] (numeric) = 0.51074266286664661890303048660562 absolute error = 0.51074266286664661890303048660562 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8752 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4127 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0 y[1] (numeric) = 0.51750557876690544838377245425549 absolute error = 0.51750557876690544838377245425549 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8868 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4255 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0 y[1] (numeric) = 0.52424764323547939382768686864791 absolute error = 0.52424764323547939382768686864791 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8983 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4382 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0 y[1] (numeric) = 0.53096910069333606130271941698923 absolute error = 0.53096910069333606130271941698923 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9098 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4509 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0 y[1] (numeric) = 0.53767019151881892861421714078181 absolute error = 0.53767019151881892861421714078181 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9214 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4635 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop bytes used=64019124, alloc=4390108, time=2.07 x[1] = 0.81 y[1] (analytic) = 0 y[1] (numeric) = 0.54435115215420092407360306229623 absolute error = 0.54435115215420092407360306229623 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9329 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4762 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0 y[1] (numeric) = 0.55101221520830338550260697511555 absolute error = 0.55101221520830338550260697511555 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9444 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4889 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0 y[1] (numeric) = 0.55765360955536999295450432227815 absolute error = 0.55765360955536999295450432227815 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.956 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5015 Order of pole (six term test) = -1.074 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0 y[1] (numeric) = 0.56427556043037397567630861492222 absolute error = 0.56427556043037397567630861492222 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9675 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5141 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0 y[1] (numeric) = 0.57087828952092640075386723913083 absolute error = 0.57087828952092640075386723913083 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.979 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5268 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0 y[1] (numeric) = 0.57746201505594359217071122068262 absolute error = 0.57746201505594359217071122068262 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9905 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5394 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop bytes used=68020260, alloc=4390108, time=2.20 x[1] = 0.87 y[1] (analytic) = 0 y[1] (numeric) = 0.58402695189122264524041501540742 absolute error = 0.58402695189122264524041501540742 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.002 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5521 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0 y[1] (numeric) = 0.59057331159206553855650877387381 absolute error = 0.59057331159206553855650877387381 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.014 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 = 0.5647 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0 y[1] (numeric) = 0.59710130251308445464915053122918 absolute error = 0.59710130251308445464915053122918 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.025 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 = 0.5774 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0 y[1] (numeric) = 0.60361112987531355674576728389863 absolute error = 0.60361112987531355674576728389863 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.037 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.59 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0 y[1] (numeric) = 0.61010299584074559166330751603101 absolute error = 0.61010299584074559166330751603101 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.048 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6027 Order of pole (six term test) = -1.073 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0 y[1] (numeric) = 0.61657709958440526073922802770408 absolute error = 0.61657709958440526073922802770408 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=72022456, alloc=4390108, time=2.33 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6153 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0 y[1] (numeric) = 0.62303363736406528788231547703218 absolute error = 0.62303363736406528788231547703218 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.071 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.628 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0 y[1] (numeric) = 0.62947280258770548524643451516155 absolute error = 0.62947280258770548524643451516155 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.083 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6407 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0 y[1] (numeric) = 0.63589478587880984428414528068646 absolute error = 0.63589478587880984428414528068646 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.094 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6534 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0 y[1] (numeric) = 0.64229977513959173698848708357534 absolute error = 0.64229977513959173698848708357534 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.106 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6661 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0 y[1] (numeric) = 0.64868795561223267510485293698418 absolute error = 0.64868795561223267510485293698418 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.117 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6788 Order of pole (six term test) = -1.072 TOP MAIN SOLVE Loop bytes used=76023704, alloc=4390108, time=2.46 x[1] = 0.98 y[1] (analytic) = 0 y[1] (numeric) = 0.65505950993821572207493371639918 absolute error = 0.65505950993821572207493371639918 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.129 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6915 Order of pole (six term test) = -1.071 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0 y[1] (numeric) = 0.66141461821583056332533399809124 absolute error = 0.66141461821583056332533399809124 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7043 Order of pole (six term test) = -1.071 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0 y[1] (numeric) = 0.66775345805592339671748788487261 absolute error = 0.66775345805592339671748788487261 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.152 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.717 Order of pole (six term test) = -1.071 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0 y[1] (numeric) = 0.67407620463596118948926057076725 absolute error = 0.67407620463596118948926057076725 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.164 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7298 Order of pole (six term test) = -1.071 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0 y[1] (numeric) = 0.68038303075247644514108579639966 absolute error = 0.68038303075247644514108579639966 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.175 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7426 Order of pole (six term test) = -1.071 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0 y[1] (numeric) = 0.686674106871955418974240403368 absolute error = 0.686674106871955418974240403368 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.187 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7553 Order of pole (six term test) = -1.071 TOP MAIN SOLVE Loop bytes used=80024764, alloc=4455632, time=2.59 x[1] = 1.04 y[1] (analytic) = 0 y[1] (numeric) = 0.69294960118022970101747172123059 absolute error = 0.69294960118022970101747172123059 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.198 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7681 Order of pole (six term test) = -1.07 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0 y[1] (numeric) = 0.69920967963042823754386678486906 absolute error = 0.69920967963042823754386678486906 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.21 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 = 0.781 Order of pole (six term test) = -1.07 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0 y[1] (numeric) = 0.70545450598954417588017711812902 absolute error = 0.70545450598954417588017711812902 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.221 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7938 Order of pole (six term test) = -1.07 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0 y[1] (numeric) = 0.71168424188366838119876660140558 absolute error = 0.71168424188366838119876660140558 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.233 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8066 Order of pole (six term test) = -1.07 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0 y[1] (numeric) = 0.71789904684193907869464805484975 absolute error = 0.71789904684193907869464805484975 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.244 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8195 Order of pole (six term test) = -1.07 TOP MAIN SOLVE Loop bytes used=84027228, alloc=4455632, time=2.72 x[1] = 1.09 y[1] (analytic) = 0 y[1] (numeric) = 0.72409907833925481094213881089573 absolute error = 0.72409907833925481094213881089573 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.256 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8324 Order of pole (six term test) = -1.069 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.73028449183779575991254456114992 absolute error = 0.73028449183779575991254456114992 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.267 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8453 Order of pole (six term test) = -1.069 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0 y[1] (numeric) = 0.73645544082739645833692187347408 absolute error = 0.73645544082739645833692187347408 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.279 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8582 Order of pole (six term test) = -1.069 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0 y[1] (numeric) = 0.74261207686481099859432049614207 absolute error = 0.74261207686481099859432049614207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8711 Order of pole (six term test) = -1.069 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0 y[1] (numeric) = 0.7487545496119100323863666085413 absolute error = 0.7487545496119100323863666085413 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.302 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 = 0.884 Order of pole (six term test) = -1.069 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0 y[1] (numeric) = 0.75488300687284713488585148811905 absolute error = 0.75488300687284713488585148811905 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.313 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 = 0.897 Order of pole (six term test) = -1.068 TOP MAIN SOLVE Loop bytes used=88028644, alloc=4455632, time=2.86 x[1] = 1.15 y[1] (analytic) = 0 y[1] (numeric) = 0.7609975946302304770171380383122 absolute error = 0.7609975946302304770171380383122 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.325 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9099 Order of pole (six term test) = -1.068 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0 y[1] (numeric) = 0.76709845708033420363760452841922 absolute error = 0.76709845708033420363760452841922 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.337 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9229 Order of pole (six term test) = -1.068 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0 y[1] (numeric) = 0.77318573666738244860989154048868 absolute error = 0.77318573666738244860989154048868 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.348 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9359 Order of pole (six term test) = -1.068 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0 y[1] (numeric) = 0.77925957411693752539394096221576 absolute error = 0.77925957411693752539394096221576 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9489 Order of pole (six term test) = -1.067 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0 y[1] (numeric) = 0.78532010846842250947098648466503 absolute error = 0.78532010846842250947098648466503 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.371 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 = 0.9619 Order of pole (six term test) = -1.067 TOP MAIN SOLVE Loop bytes used=92029644, alloc=4455632, time=2.99 x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 0.79136747710680717255602953696215 absolute error = 0.79136747710680717255602953696215 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.383 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9749 Order of pole (six term test) = -1.067 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0 y[1] (numeric) = 0.79740181579348503434837440640788 absolute error = 0.79740181579348503434837440640788 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.394 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.988 Order of pole (six term test) = -1.067 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0 y[1] (numeric) = 0.80342325869636816194918202882353 absolute error = 0.80342325869636816194918202882353 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.406 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.001 Order of pole (six term test) = -1.067 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0 y[1] (numeric) = 0.80943193841922526671027849292824 absolute error = 0.80943193841922526671027849292824 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.417 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.014 Order of pole (six term test) = -1.066 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0 y[1] (numeric) = 0.81542798603028762005416221045208 absolute error = 0.81542798603028762005416221045208 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.429 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.027 Order of pole (six term test) = -1.066 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0 y[1] (numeric) = 0.82141153109014633080531502283197 absolute error = 0.82141153109014633080531502283197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.04 Order of pole (six term test) = -1.066 TOP MAIN SOLVE Loop bytes used=96031736, alloc=4455632, time=3.12 x[1] = 1.26 y[1] (analytic) = 0 y[1] (numeric) = 0.82738270167896359406676252020645 absolute error = 0.82738270167896359406676252020645 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.452 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.053 Order of pole (six term test) = -1.066 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0 y[1] (numeric) = 0.83334162442301963310462591234316 absolute error = 0.83334162442301963310462591234316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.463 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.067 Order of pole (six term test) = -1.065 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0 y[1] (numeric) = 0.83928842452061620866837407235562 absolute error = 0.83928842452061620866837407235562 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.475 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 = 1.08 Order of pole (six term test) = -1.065 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0 y[1] (numeric) = 0.84522322576735676242558900332127 absolute error = 0.84522322576735676242558900332127 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.487 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 = 1.093 Order of pole (six term test) = -1.065 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 0.8511461505808224906157126452939 absolute error = 0.8511461505808224906157126452939 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.498 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 = 1.106 Order of pole (six term test) = -1.065 TOP MAIN SOLVE Loop bytes used=100032532, alloc=4455632, time=3.25 x[1] = 1.31 y[1] (analytic) = 0 y[1] (numeric) = 0.85705732002466290864477715667981 absolute error = 0.85705732002466290864477715667981 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.119 Order of pole (six term test) = -1.065 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0 y[1] (numeric) = 0.86295685383211876528998075900613 absolute error = 0.86295685383211876528998075900613 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.521 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.132 Order of pole (six term test) = -1.064 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0 y[1] (numeric) = 0.86884487042899449470858216369781 absolute error = 0.86884487042899449470858216369781 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.533 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 = 1.146 Order of pole (six term test) = -1.064 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0 y[1] (numeric) = 0.87472148695609675390382398616772 absolute error = 0.87472148695609675390382398616772 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.544 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 = 1.159 Order of pole (six term test) = -1.064 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0 y[1] (numeric) = 0.88058681929115498114281536384138 absolute error = 0.88058681929115498114281536384138 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.556 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 = 1.172 Order of pole (six term test) = -1.064 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0 y[1] (numeric) = 0.88644098207023932558988658004995 absolute error = 0.88644098207023932558988658004995 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.567 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 = 1.185 Order of pole (six term test) = -1.063 TOP MAIN SOLVE Loop bytes used=104033332, alloc=4455632, time=3.39 x[1] = 1.37 y[1] (analytic) = 0 y[1] (numeric) = 0.89228408870869073874129475527963 absolute error = 0.89228408870869073874129475527963 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.579 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.199 Order of pole (six term test) = -1.063 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0 y[1] (numeric) = 0.89811625142157748283022172200509 absolute error = 0.89811625142157748283022172200509 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.212 Order of pole (six term test) = -1.063 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0 y[1] (numeric) = 0.90393758124369179899601706518642 absolute error = 0.90393758124369179899601706518642 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.602 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.225 Order of pole (six term test) = -1.063 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 0.90974818804909998752941605023574 absolute error = 0.90974818804909998752941605023574 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.613 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.239 Order of pole (six term test) = -1.062 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0 y[1] (numeric) = 0.91554818057025868283193868018516 absolute error = 0.91554818057025868283193868018516 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.625 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.252 Order of pole (six term test) = -1.062 TOP MAIN SOLVE Loop bytes used=108034252, alloc=4455632, time=3.52 x[1] = 1.42 y[1] (analytic) = 0 y[1] (numeric) = 0.92133766641670965583977922903802 absolute error = 0.92133766641670965583977922903802 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.637 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.265 Order of pole (six term test) = -1.062 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0 y[1] (numeric) = 0.9271167520933650455943051430532 absolute error = 0.9271167520933650455943051430532 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.648 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.279 Order of pole (six term test) = -1.062 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0 y[1] (numeric) = 0.93288554301839450848046119227244 absolute error = 0.93288554301839450848046119227244 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.292 Order of pole (six term test) = -1.061 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0 y[1] (numeric) = 0.93864414354072537753883610199798 absolute error = 0.93864414354072537753883610199798 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.671 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.305 Order of pole (six term test) = -1.061 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0 y[1] (numeric) = 0.94439265695716654437197018791336 absolute error = 0.94439265695716654437197018791336 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.319 Order of pole (six term test) = -1.061 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 0 y[1] (numeric) = 0.95013118552916641174001172026672 absolute error = 0.95013118552916641174001172026672 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.694 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.332 Order of pole (six term test) = -1.061 TOP MAIN SOLVE Loop bytes used=112035200, alloc=4455632, time=3.66 x[1] = 1.48 y[1] (analytic) = 0 y[1] (numeric) = 0.95585983049921491524599608483318 absolute error = 0.95585983049921491524599608483318 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.706 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.346 Order of pole (six term test) = -1.06 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0 y[1] (numeric) = 0.96157869210689927685682546181856 absolute error = 0.96157869210689927685682546181856 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.717 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.359 Order of pole (six term test) = -1.06 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 0.96728786960462283073919596584147 absolute error = 0.96728786960462283073919596584147 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.729 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.372 Order of pole (six term test) = -1.06 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 0 y[1] (numeric) = 0.97298746127299595239152273279279 absolute error = 0.97298746127299595239152273279279 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.386 Order of pole (six term test) = -1.06 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0 y[1] (numeric) = 0.97867756443590782473711696037114 absolute error = 0.97867756443590782473711696037114 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.752 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.399 Order of pole (six term test) = -1.059 TOP MAIN SOLVE Loop bytes used=116036196, alloc=4455632, time=3.79 x[1] = 1.53 y[1] (analytic) = 0 y[1] (numeric) = 0.98435827547528748915482501415909 absolute error = 0.98435827547528748915482501415909 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.764 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 = 1.413 Order of pole (six term test) = -1.059 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0 y[1] (numeric) = 0.99002968984556235483420206795317 absolute error = 0.99002968984556235483420206795317 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.775 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 = 1.426 Order of pole (six term test) = -1.059 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0 y[1] (numeric) = 0.99569190208782207585334545217044 absolute error = 0.99569190208782207585334545217044 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.787 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.44 Order of pole (six term test) = -1.059 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 0 y[1] (numeric) = 1.0013450058436954515146069440227 absolute error = 1.0013450058436954515146069440227 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.798 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.453 Order of pole (six term test) = -1.058 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0 y[1] (numeric) = 1.0069890938689477612864926451678 absolute error = 1.0069890938689477612864926451678 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.467 Order of pole (six term test) = -1.058 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0 y[1] (numeric) = 1.0126242580468057107618295827354 absolute error = 1.0126242580468057107618295827354 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.821 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.48 Order of pole (six term test) = -1.058 TOP MAIN SOLVE Loop bytes used=120037176, alloc=4455632, time=3.92 x[1] = 1.59 y[1] (analytic) = 0 y[1] (numeric) = 1.0182505894010169389468621695869 absolute error = 1.0182505894010169389468621695869 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.833 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.494 Order of pole (six term test) = -1.058 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 1.0238681781086508195577135875437 absolute error = 1.0238681781086508195577135875437 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.844 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.507 Order of pole (six term test) = -1.058 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0 y[1] (numeric) = 1.0294771135126470794530935106738 absolute error = 1.0294771135126470794530935106738 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.856 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.521 Order of pole (six term test) = -1.057 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0 y[1] (numeric) = 1.0350774841341185555267927621293 absolute error = 1.0350774841341185555267927621293 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.867 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.535 Order of pole (six term test) = -1.057 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0 y[1] (numeric) = 1.0406693776844142169889726338414 absolute error = 1.0406693776844142169889726338414 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.879 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.548 Order of pole (six term test) = -1.057 TOP MAIN SOLVE Loop bytes used=124038324, alloc=4455632, time=4.05 x[1] = 1.64 y[1] (analytic) = 0 y[1] (numeric) = 1.0462528810769483926662490616848 absolute error = 1.0462528810769483926662490616848 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.562 Order of pole (six term test) = -1.057 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0 y[1] (numeric) = 1.0518280804388019624470513401654 absolute error = 1.0518280804388019624470513401654 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.902 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.575 Order of pole (six term test) = -1.056 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0 y[1] (numeric) = 1.0573950611221010980050825689143 absolute error = 1.0573950611221010980050825689143 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.914 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.589 Order of pole (six term test) = -1.056 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 0 y[1] (numeric) = 1.0629539077151789701779491519618 absolute error = 1.0629539077151789701779491519618 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.925 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.603 Order of pole (six term test) = -1.056 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0 y[1] (numeric) = 1.0685047040535256786010981031136 absolute error = 1.0685047040535256786010981031136 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.937 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.616 Order of pole (six term test) = -1.056 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0 y[1] (numeric) = 1.074047533230531503152270007494 absolute error = 1.074047533230531503152270007494 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.948 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.63 Order of pole (six term test) = -1.055 TOP MAIN SOLVE Loop bytes used=128039564, alloc=4521156, time=4.19 x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 1.0795824776080284262134902285581 absolute error = 1.0795824776080284262134902285581 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.96 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 = 1.644 Order of pole (six term test) = -1.055 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0 y[1] (numeric) = 1.085109618826634729481902613073 absolute error = 1.085109618826634729481902613073 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.971 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 = 1.657 Order of pole (six term test) = -1.055 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0 y[1] (numeric) = 1.0906290378159073288436201365894 absolute error = 1.0906290378159073288436201365894 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.983 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.671 Order of pole (six term test) = -1.055 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0 y[1] (numeric) = 1.0961408148043063754622076763122 absolute error = 1.0961408148043063754622076763122 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.994 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.685 Order of pole (six term test) = -1.054 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0 y[1] (numeric) = 1.1016450293289765205307569464071 absolute error = 1.1016450293289765205307569464071 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.006 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.698 Order of pole (six term test) = -1.054 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0 y[1] (numeric) = 1.1071417602453491149079677967574 absolute error = 1.1071417602453491149079677967574 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=132040816, alloc=4521156, time=4.32 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.017 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.712 Order of pole (six term test) = -1.054 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0 y[1] (numeric) = 1.1126310857365694929268378125571 absolute error = 1.1126310857365694929268378125571 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.029 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.726 Order of pole (six term test) = -1.054 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0 y[1] (numeric) = 1.1181130833227533718600996623977 absolute error = 1.1181130833227533718600996623977 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.041 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.74 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0 y[1] (numeric) = 1.1235878298700762846876379547631 absolute error = 1.1235878298700762846876379547631 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.052 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.753 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0 y[1] (numeric) = 1.1290554015996998537831776925289 absolute error = 1.1290554015996998537831776925289 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.064 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.767 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 1.1345158740965386067728266431487 absolute error = 1.1345158740965386067728266431487 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.075 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.781 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop bytes used=136042788, alloc=4521156, time=4.45 x[1] = 1.81 y[1] (analytic) = 0 y[1] (numeric) = 1.1399693223178709329753449261925 absolute error = 1.1399693223178709329753449261925 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.087 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.795 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0 y[1] (numeric) = 1.1454158206017976793782656395395 absolute error = 1.1454158206017976793782656395395 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.098 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 = 1.808 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0 y[1] (numeric) = 1.150855442675551788906043563924 absolute error = 1.150855442675551788906043563924 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.822 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0 y[1] (numeric) = 1.156288261663662290672705379174 absolute error = 1.156288261663662290672705379174 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.121 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.836 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 0 y[1] (numeric) = 1.1617143500959758618637806046774 absolute error = 1.1617143500959758618637806046774 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.133 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.85 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0 y[1] (numeric) = 1.1671337799155390937474425809998 absolute error = 1.1671337799155390937474425809998 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.144 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.864 Order of pole (six term test) = -1.051 bytes used=140044696, alloc=4521156, time=4.59 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0 y[1] (numeric) = 1.17254662248634450996444362205 absolute error = 1.17254662248634450996444362205 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.156 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.877 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0 y[1] (numeric) = 1.1779529486009433035868434442982 absolute error = 1.1779529486009433035868434442982 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.168 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.891 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0 y[1] (numeric) = 1.1833528284879276803673374473553 absolute error = 1.1833528284879276803673374473553 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.179 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.905 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0 y[1] (numeric) = 1.1887463318192856190289938320003 absolute error = 1.1887463318192856190289938320003 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.191 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.919 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0 y[1] (numeric) = 1.1941335277176307852781825381403 absolute error = 1.1941335277176307852781825381403 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.202 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.933 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop bytes used=144045560, alloc=4521156, time=4.72 x[1] = 1.92 y[1] (analytic) = 0 y[1] (numeric) = 1.1995144847633102643739896386204 absolute error = 1.1995144847633102643739896386204 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.214 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.947 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 0 y[1] (numeric) = 1.2048892710013927074716354883483 absolute error = 1.2048892710013927074716354883483 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.225 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.96 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0 y[1] (numeric) = 1.2102579539485394194949761450432 absolute error = 1.2102579539485394194949761450432 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.237 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 = 1.974 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0 y[1] (numeric) = 1.215620600599760850906974540929 absolute error = 1.215620600599760850906974540929 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.248 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.988 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0 y[1] (numeric) = 1.2209772774350608923631259668403 absolute error = 1.2209772774350608923631259668403 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.26 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 = 2.002 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0 y[1] (numeric) = 1.2263280504259713097802503358936 absolute error = 1.2263280504259713097802503358936 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.271 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = -1.049 bytes used=148047336, alloc=4521156, time=4.85 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0 y[1] (numeric) = 1.2316729850419785977637178082594 absolute error = 1.2316729850419785977637178082594 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.283 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 = 2.03 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0 y[1] (numeric) = 1.2370121462568454715446798977111 absolute error = 1.2370121462568454715446798977111 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.295 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.044 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.242345598554829161522466768887 absolute error = 1.242345598554829161522466768887 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.306 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 = 2.058 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 0 y[1] (numeric) = 1.2476734059367986201257047577451 absolute error = 1.2476734059367986201257047577451 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.318 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 = 2.072 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0 y[1] (numeric) = 1.2529956319262526979410073537133 absolute error = 1.2529956319262526979410073537133 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.329 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.086 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop bytes used=152048068, alloc=4521156, time=4.98 x[1] = 2.03 y[1] (analytic) = 0 y[1] (numeric) = 1.2583123395752412948546734129321 absolute error = 1.2583123395752412948546734129321 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.341 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.1 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0 y[1] (numeric) = 1.2636235914701914422572379417936 absolute error = 1.2636235914701914422572379417936 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.352 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.114 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0 y[1] (numeric) = 1.2689294497376402241215922277866 absolute error = 1.2689294497376402241215922277866 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.364 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.128 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 0 y[1] (numeric) = 1.2742299760498763979333387954039 absolute error = 1.2742299760498763979333387954039 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.375 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.142 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0 y[1] (numeric) = 1.2795252316304925309795924032319 absolute error = 1.2795252316304925309795924032319 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.387 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.156 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0 y[1] (numeric) = 1.2848152772598494233439211753869 absolute error = 1.2848152772598494233439211753869 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.399 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.17 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop bytes used=156049416, alloc=4521156, time=5.11 x[1] = 2.09 y[1] (analytic) = 0 y[1] (numeric) = 1.2901001732804545460666242658819 absolute error = 1.2901001732804545460666242658819 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.184 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0 y[1] (numeric) = 1.2953799796022561812688142398466 absolute error = 1.2953799796022561812688142398466 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.422 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.198 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0 y[1] (numeric) = 1.3006547557078549105651605252147 absolute error = 1.3006547557078549105651605252147 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.433 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.212 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0 y[1] (numeric) = 1.3059245606576340587645310265718 absolute error = 1.3059245606576340587645310265718 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.445 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.226 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0 y[1] (numeric) = 1.3111894530948106616424833534672 absolute error = 1.3111894530948106616424833534672 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.456 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.24 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop bytes used=160050124, alloc=4521156, time=5.25 x[1] = 2.14 y[1] (analytic) = 0 y[1] (numeric) = 1.3164494912504084894283496148161 absolute error = 1.3164494912504084894283496148161 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.468 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.254 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 0 y[1] (numeric) = 1.3217047329481546215476187874952 absolute error = 1.3217047329481546215476187874952 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.479 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.268 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0 y[1] (numeric) = 1.3269552356093010330638267452044 absolute error = 1.3269552356093010330638267452044 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.491 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.282 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0 y[1] (numeric) = 1.332201056257372619140830353828 absolute error = 1.332201056257372619140830353828 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.502 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.296 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0 y[1] (numeric) = 1.3374422515228430506649677268342 absolute error = 1.3374422515228430506649677268342 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.514 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.31 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0 y[1] (numeric) = 1.3426788776477398218971272812108 absolute error = 1.3426788776477398218971272812108 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.526 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.324 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop bytes used=164050968, alloc=4521156, time=5.38 x[1] = 2.2 y[1] (analytic) = 0 y[1] (numeric) = 1.3479109904901798196381891642271 absolute error = 1.3479109904901798196381891642271 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.537 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.338 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0 y[1] (numeric) = 1.3531386455288367128597352415133 absolute error = 1.3531386455288367128597352415133 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.549 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.352 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0 y[1] (numeric) = 1.3583618978673414320484229804952 absolute error = 1.3583618978673414320484229804952 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.366 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0 y[1] (numeric) = 1.3635808022386169786110222188387 absolute error = 1.3635808022386169786110222188387 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.572 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.38 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0 y[1] (numeric) = 1.3687954130091487765627845470618 absolute error = 1.3687954130091487765627845470618 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.583 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.394 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop bytes used=168051920, alloc=4521156, time=5.51 x[1] = 2.25 y[1] (analytic) = 0 y[1] (numeric) = 1.3740057841831917513504031493213 absolute error = 1.3740057841831917513504031493213 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.595 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.408 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0 y[1] (numeric) = 1.3792119694069152940190292105049 absolute error = 1.3792119694069152940190292105049 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.606 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.422 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0 y[1] (numeric) = 1.3844140219724872429981609779768 absolute error = 1.3844140219724872429981609779768 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.618 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.437 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 0 y[1] (numeric) = 1.3896119948220979905320214059925 absolute error = 1.3896119948220979905320214059925 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.629 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 = 2.451 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0 y[1] (numeric) = 1.3948059405519257961953539159653 absolute error = 1.3948059405519257961953539159653 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.641 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.465 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0 y[1] (numeric) = 1.399995911416044365995183367033 absolute error = 1.399995911416044365995183367033 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.653 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.479 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop bytes used=172053456, alloc=4521156, time=5.64 x[1] = 2.31 y[1] (analytic) = 0 y[1] (numeric) = 1.4051819593302737322434991179525 absolute error = 1.4051819593302737322434991179525 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.664 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.493 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0 y[1] (numeric) = 1.4103641358759754466761784271897 absolute error = 1.4103641358759754466761784271897 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.676 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 = 2.507 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 0 y[1] (numeric) = 1.4155424923037930771715859829391 absolute error = 1.4155424923037930771715859829391 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.687 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 = 2.521 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0 y[1] (numeric) = 1.4207170795373389768705841862379 absolute error = 1.4207170795373389768705841862379 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.699 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.536 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0 y[1] (numeric) = 1.4258879481768282735011908549689 absolute error = 1.4258879481768282735011908549689 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.55 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop bytes used=176054412, alloc=4521156, time=5.77 x[1] = 2.36 y[1] (analytic) = 0 y[1] (numeric) = 1.4310551485026610062494223321408 absolute error = 1.4310551485026610062494223321408 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.722 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.564 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0 y[1] (numeric) = 1.4362187304789533175771090236187 absolute error = 1.4362187304789533175771090236187 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.733 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.578 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0 y[1] (numeric) = 1.44137874375701858795234718781 absolute error = 1.44137874375701858795234718781 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.745 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 = 2.592 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0 y[1] (numeric) = 1.4465352376787993825139470014235 absolute error = 1.4465352376787993825139470014235 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 = 2.606 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0 y[1] (numeric) = 1.4516882612802510602234366734991 absolute error = 1.4516882612802510602234366734991 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.768 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.621 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0 y[1] (numeric) = 1.4568378632946778780530439753027 absolute error = 1.4568378632946778780530439753027 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 = 2.635 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop bytes used=180055436, alloc=4521156, time=5.91 x[1] = 2.42 y[1] (analytic) = 0 y[1] (numeric) = 1.4619840921560224052022148763962 absolute error = 1.4619840921560224052022148763962 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.791 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.649 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0 y[1] (numeric) = 1.4671269960021090452156986280067 absolute error = 1.4671269960021090452156986280067 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 = 2.663 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0 y[1] (numeric) = 1.4722666226778424471805077657118 absolute error = 1.4722666226778424471805077657118 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.814 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.677 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0 y[1] (numeric) = 1.4774030197383615708950363058849 absolute error = 1.4774030197383615708950363058849 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 = 2.692 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 0 y[1] (numeric) = 1.4825362344521501550195692321563 absolute error = 1.4825362344521501550195692321563 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.837 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.706 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop bytes used=184056540, alloc=4521156, time=6.04 x[1] = 2.47 y[1] (analytic) = 0 y[1] (numeric) = 1.487666313804104321721999431095 absolute error = 1.487666313804104321721999431095 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 = 2.72 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 0 y[1] (numeric) = 1.4927933044985580362148079277336 absolute error = 1.4927933044985580362148079277336 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 = 2.734 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 0 y[1] (numeric) = 1.497917252962267124828634984772 absolute error = 1.497917252962267124828634984772 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 = 2.749 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0 y[1] (numeric) = 1.5030382053473525408737881288174 absolute error = 1.5030382053473525408737881288174 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 = 2.763 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 0 y[1] (numeric) = 1.5081562075342035534938404555149 absolute error = 1.5081562075342035534938404555149 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 = 2.777 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0 y[1] (numeric) = 1.513271305134341521005426230641 absolute error = 1.513271305134341521005426230641 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 = 2.791 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop bytes used=188057816, alloc=4521156, time=6.17 x[1] = 2.53 y[1] (analytic) = 0 y[1] (numeric) = 1.5183835434932448968361028250782 absolute error = 1.5183835434932448968361028250782 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 = 2.806 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0 y[1] (numeric) = 1.523492967693136103108674013531 absolute error = 1.523492967693136103108674013531 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 = 2.82 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 0 y[1] (numeric) = 1.5285996225557308941668985477409 absolute error = 1.5285996225557308941668985477409 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.941 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 = 2.834 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 0 y[1] (numeric) = 1.5337035526449508198855519733053 absolute error = 1.5337035526449508198855519733053 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 = 2.848 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0 y[1] (numeric) = 1.5388048022695993864491450076173 absolute error = 1.5388048022695993864491450076173 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.964 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 = 2.863 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop bytes used=192058660, alloc=4521156, time=6.30 x[1] = 2.58 y[1] (analytic) = 0 y[1] (numeric) = 1.5439034154860025004102591940061 absolute error = 1.5439034154860025004102591940061 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 = 2.877 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0 y[1] (numeric) = 1.5489994361006137702427165750288 absolute error = 1.5489994361006137702427165750288 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 = 2.891 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 0 y[1] (numeric) = 1.554092907672585228279168703204 absolute error = 1.554092907672585228279168703204 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 = 2.906 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0 y[1] (numeric) = 1.5591838735163040248599145215272 absolute error = 1.5591838735163040248599145215272 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 = 2.92 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0 y[1] (numeric) = 1.5642723767038956357128009128086 absolute error = 1.5642723767038956357128009128086 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 = 2.934 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0 y[1] (numeric) = 1.5693584600676941130261022191051 absolute error = 1.5693584600676941130261022191051 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 = 2.948 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop bytes used=196059752, alloc=4521156, time=6.44 x[1] = 2.64 y[1] (analytic) = 0 y[1] (numeric) = 1.5744421662026799003607004535798 absolute error = 1.5744421662026799003607004535798 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 = 2.963 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 0 y[1] (numeric) = 1.5795235374688857214682804556496 absolute error = 1.5795235374688857214682804556496 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 = 2.977 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0 y[1] (numeric) = 1.58460261599377104323239083734 absolute error = 1.58460261599377104323239083734 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 = 2.991 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0 y[1] (numeric) = 1.5896794436745656033230654863329 absolute error = 1.5896794436745656033230654863329 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 = 3.006 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0 y[1] (numeric) = 1.5947540621805824837473949317521 absolute error = 1.5947540621805824837473949317521 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.092 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 = 3.02 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop bytes used=200062152, alloc=4521156, time=6.57 x[1] = 2.69 y[1] (analytic) = 0 y[1] (numeric) = 1.5998265129555012022822993861497 absolute error = 1.5998265129555012022822993861497 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 = 3.034 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0 y[1] (numeric) = 1.6048968372196212847862713494562 absolute error = 1.6048968372196212847862713494562 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.115 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.049 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 0 y[1] (numeric) = 1.6099650759720867725986735756611 absolute error = 1.6099650759720867725986735756611 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 = 3.063 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 0 y[1] (numeric) = 1.6150312699930821106431035483541 absolute error = 1.6150312699930821106431035483541 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.138 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.077 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0 y[1] (numeric) = 1.6200954598459998534503261105261 absolute error = 1.6200954598459998534503261105261 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 = 3.092 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 0 y[1] (numeric) = 1.6251576858795806181014364210617 absolute error = 1.6251576858795806181014364210617 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 = 3.106 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop bytes used=204063408, alloc=4521156, time=6.70 x[1] = 2.75 y[1] (analytic) = 0 y[1] (numeric) = 1.6302179882300257050584931844099 absolute error = 1.6302179882300257050584931844099 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 = 3.12 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0 y[1] (numeric) = 1.6352764068230827999932420543949 absolute error = 1.6352764068230827999932420543949 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 = 3.135 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0 y[1] (numeric) = 1.6403329813761051620402494309382 absolute error = 1.6403329813761051620402494309382 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 = 3.149 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0 y[1] (numeric) = 1.6453877514000846963844346776002 absolute error = 1.6453877514000846963844346776002 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 = 3.163 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0 y[1] (numeric) = 1.6504407562016593017403960107319 absolute error = 1.6504407562016593017403960107319 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.219 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.178 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop bytes used=208064236, alloc=4521156, time=6.83 x[1] = 2.8 y[1] (analytic) = 0 y[1] (numeric) = 1.6554920348850948760879646616802 absolute error = 1.6554920348850948760879646616802 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 = 3.192 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 0 y[1] (numeric) = 1.6605416263542423569911030367637 absolute error = 1.6605416263542423569911030367637 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.242 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.207 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 0 y[1] (numeric) = 1.665589569314470165941708347017 absolute error = 1.665589569314470165941708347017 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 = 3.221 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 0 y[1] (numeric) = 1.6706359022745724194323260158856 absolute error = 1.6706359022745724194323260158856 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.265 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.235 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 0 y[1] (numeric) = 1.6756806635486532628685557096372 absolute error = 1.6756806635486532628685557096372 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 = 3.25 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0 y[1] (numeric) = 1.6807238912579876769794884847529 absolute error = 1.6807238912579876769794884847529 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.288 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.264 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop bytes used=212065336, alloc=4521156, time=6.96 x[1] = 2.86 y[1] (analytic) = 0 y[1] (numeric) = 1.6857656233328591000693872935752 absolute error = 1.6857656233328591000693872935752 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 = 3.279 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0 y[1] (numeric) = 1.6908058975143742032726523739507 absolute error = 1.6908058975143742032726523739507 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.311 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.293 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 0 y[1] (numeric) = 1.6958447513562551499236287569618 absolute error = 1.6958447513562551499236287569618 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.323 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.307 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0 y[1] (numeric) = 1.7008822222266096642298366870579 absolute error = 1.7008822222266096642298366870579 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.334 Order 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) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0 y[1] (numeric) = 1.7059183473096792286386463253517 absolute error = 1.7059183473096792286386463253517 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.346 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.336 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop bytes used=216066532, alloc=4521156, time=7.10 x[1] = 2.91 y[1] (analytic) = 0 y[1] (numeric) = 1.7109531636075657236102698913751 absolute error = 1.7109531636075657236102698913751 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.357 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.351 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 0 y[1] (numeric) = 1.7159867079419368179512839940323 absolute error = 1.7159867079419368179512839940323 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.369 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 = 3.365 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0 y[1] (numeric) = 1.721019016955710412419878795321 absolute error = 1.721019016955710412419878795321 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.38 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 = 3.379 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 0 y[1] (numeric) = 1.7260501271147184339838927690724 absolute error = 1.7260501271147184339838927690724 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.392 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.394 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0 y[1] (numeric) = 1.7310800747093502728927411728401 absolute error = 1.7310800747093502728927411728401 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.403 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.408 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0 y[1] (numeric) = 1.7361088958561761496119647587842 absolute error = 1.7361088958561761496119647587842 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.415 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.423 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop bytes used=220067560, alloc=4521156, time=7.23 x[1] = 2.97 y[1] (analytic) = 0 y[1] (numeric) = 1.7411366264995506936617651238316 absolute error = 1.7411366264995506936617651238316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.427 Order 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) = -1.034 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0 y[1] (numeric) = 1.7461633024131970114960753263699 absolute error = 1.7461633024131970114960753263699 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.438 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.452 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 0 y[1] (numeric) = 1.7511889592017715157540262747129 absolute error = 1.7511889592017715157540262747129 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.466 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 0 y[1] (numeric) = 1.756213632302409783508762642871 absolute error = 1.756213632302409783508762642871 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.461 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.48 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 0 y[1] (numeric) = 1.7612373569862537065271509119734 absolute error = 1.7612373569862537065271509119734 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.473 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.495 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop bytes used=224068824, alloc=4521156, time=7.36 x[1] = 3.02 y[1] (analytic) = 0 y[1] (numeric) = 1.7662601683599601920357814298232 absolute error = 1.7662601683599601920357814298232 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.484 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.509 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 0 y[1] (numeric) = 1.7712821013671916680616298247838 absolute error = 1.7712821013671916680616298247838 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.496 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.524 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 0 y[1] (numeric) = 1.7763031907900886430777015011674 absolute error = 1.7763031907900886430777015011674 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.507 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.538 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 0 y[1] (numeric) = 1.7813234712507245654328824954558 absolute error = 1.7813234712507245654328824954558 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.519 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.553 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 0 y[1] (numeric) = 1.786342977212543223879060687947 absolute error = 1.786342977212543223879060687947 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.531 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.567 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 0 y[1] (numeric) = 1.7913617429817789264254154573176 absolute error = 1.7913617429817789264254154573176 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.542 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.582 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop bytes used=228069676, alloc=4521156, time=7.49 x[1] = 3.08 y[1] (analytic) = 0 y[1] (numeric) = 1.7963798027088596907477042389381 absolute error = 1.7963798027088596907477042389381 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.554 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.596 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 0 y[1] (numeric) = 1.801397190389793675457553217571 absolute error = 1.801397190389793675457553217571 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.565 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.611 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 0 y[1] (numeric) = 1.8064139398675390776913864528287 absolute error = 1.8064139398675390776913864528287 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.577 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 = 3.625 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 0 y[1] (numeric) = 1.8114300848333577187089494066845 absolute error = 1.8114300848333577187089494066845 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.588 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 = 3.639 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 0 y[1] (numeric) = 1.8164456588281525354956904876663 absolute error = 1.8164456588281525354956904876663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.6 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 = 3.654 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=232070932, alloc=4521156, time=7.62 x[1] = 3.13 y[1] (analytic) = 0 y[1] (numeric) = 1.8214606952437891927398929884047 absolute error = 1.8214606952437891927398929884047 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.611 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 = 3.668 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 0 y[1] (numeric) = 1.8264752273244020260027773314388 absolute error = 1.8264752273244020260027773314388 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.623 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.683 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 0 y[1] (numeric) = 1.8314892881676845234162388151224 absolute error = 1.8314892881676845234162388151224 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.634 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.697 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 0 y[1] (numeric) = 1.8365029107261645498269081569178 absolute error = 1.8365029107261645498269081569178 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.646 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.712 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0 y[1] (numeric) = 1.8415161278084645139553191435769 absolute error = 1.8415161278084645139553191435769 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.658 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.726 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0 y[1] (numeric) = 1.8465289720805466758536755804006 absolute error = 1.8465289720805466758536755804006 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.669 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.741 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=236072036, alloc=4521156, time=7.75 x[1] = 3.19 y[1] (analytic) = 0 y[1] (numeric) = 1.8515414760669437887236012655506 absolute error = 1.8515414760669437887236012655506 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.681 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.755 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0 y[1] (numeric) = 1.8565536721519752659949404625702 absolute error = 1.8565536721519752659949404625702 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.692 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.77 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 0 y[1] (numeric) = 1.861565592580949061466795645833 absolute error = 1.861565592580949061466795645833 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.704 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 = 3.784 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0 y[1] (numeric) = 1.8665772694613494472712212972974 absolute error = 1.8665772694613494472712212972974 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.715 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 = 3.799 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 0 y[1] (numeric) = 1.8715887347640108714370472512521 absolute error = 1.8715887347640108714370472512521 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.727 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.813 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=240074292, alloc=4521156, time=7.89 x[1] = 3.24 y[1] (analytic) = 0 y[1] (numeric) = 1.876600020324278073904924481195 absolute error = 1.876600020324278073904924481195 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.738 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.828 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0 y[1] (numeric) = 1.8816111578431526369736433312008 absolute error = 1.8816111578431526369736433312008 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.842 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0 y[1] (numeric) = 1.8866221788884261433408722540464 absolute error = 1.8866221788884261433408722540464 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.762 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.857 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0 y[1] (numeric) = 1.8916331148958001121375367487024 absolute error = 1.8916331148958001121375367487024 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.773 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.871 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 0 y[1] (numeric) = 1.896643997169992880642964580793 absolute error = 1.896643997169992880642964580793 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.785 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.886 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0 y[1] (numeric) = 1.9016548568858335967065535012187 absolute error = 1.9016548568858335967065535012187 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.796 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.901 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=244075028, alloc=4521156, time=8.02 x[1] = 3.3 y[1] (analytic) = 0 y[1] (numeric) = 1.9066657250893434842899875618212 absolute error = 1.9066657250893434842899875618212 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.808 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 = 3.915 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0 y[1] (numeric) = 1.9116766326988045419808800705318 absolute error = 1.9116766326988045419808800705318 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.819 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 = 3.93 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0 y[1] (numeric) = 1.9166876105058158318131231227547 absolute error = 1.9166876105058158318131231227547 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.831 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.944 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 0 y[1] (numeric) = 1.9216986891763375132601682729982 absolute error = 1.9216986891763375132601682729982 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.842 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.959 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0 y[1] (numeric) = 1.9267098992517227748439672733708 absolute error = 1.9267098992517227748439672733708 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.854 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 = 3.973 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=248076024, alloc=4521156, time=8.15 x[1] = 3.35 y[1] (analytic) = 0 y[1] (numeric) = 1.9317212711497378134234064749967 absolute error = 1.9317212711497378134234064749967 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.866 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.988 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 0 y[1] (numeric) = 1.9367328351655700088908369735048 absolute error = 1.9367328351655700088908369735048 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.877 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.002 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0 y[1] (numeric) = 1.9417446214728244397128207136229 absolute error = 1.9417446214728244397128207136229 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.889 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.017 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 0 y[1] (numeric) = 1.9467566601245088825005881130449 absolute error = 1.9467566601245088825005881130449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.031 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 0 y[1] (numeric) = 1.9517689810540074365860640365761 absolute error = 1.9517689810540074365860640365761 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.912 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.046 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0 y[1] (numeric) = 1.9567816140760429124098154540474 absolute error = 1.9567816140760429124098154540474 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.923 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.06 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=252077020, alloc=4521156, time=8.29 x[1] = 3.41 y[1] (analytic) = 0 y[1] (numeric) = 1.9617945888876281203970752030567 absolute error = 1.9617945888876281203970752030567 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.935 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.075 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 0 y[1] (numeric) = 1.9668079350690061949062908230017 absolute error = 1.9668079350690061949062908230017 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.946 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.09 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0 y[1] (numeric) = 1.9718216820845800857806433094417 absolute error = 1.9718216820845800857806433094417 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.958 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 = 4.104 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0 y[1] (numeric) = 1.9768358592838313480159042455687 absolute error = 1.9768358592838313480159042455687 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.119 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0 y[1] (numeric) = 1.981850495902228358077095513706 absolute error = 1.981850495902228358077095513706 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.981 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 = 4.133 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=256078040, alloc=4521156, time=8.42 x[1] = 3.46 y[1] (analytic) = 0 y[1] (numeric) = 1.986865621062124083450945643206 absolute error = 1.986865621062124083450945643206 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 3.993 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.148 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 0 y[1] (numeric) = 1.991881263773643530110379880526 absolute error = 1.991881263773643530110379880526 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.004 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.162 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0 y[1] (numeric) = 1.9968974529355609906905329980549 absolute error = 1.9968974529355609906905329980549 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.016 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.177 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 0 y[1] (numeric) = 2.00191421733616721433234664245 absolute error = 2.00191421733616721433234664245 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.027 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.192 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 0 y[1] (numeric) = 2.0069315856541266173390344214534 absolute error = 2.0069315856541266173390344214534 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.039 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.206 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 0 y[1] (numeric) = 2.0119495864593246520119111035855 absolute error = 2.0119495864593246520119111035855 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.221 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=260078800, alloc=4521156, time=8.55 x[1] = 3.52 y[1] (analytic) = 0 y[1] (numeric) = 2.0169682482137054492846454289863 absolute error = 2.0169682482137054492846454289863 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.062 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.235 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0 y[1] (numeric) = 2.0219875992720998490582818979049 absolute error = 2.0219875992720998490582818979049 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.073 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.25 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0 y[1] (numeric) = 2.0270076678830439304527725639439 absolute error = 2.0270076678830439304527725639439 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.085 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.264 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0 y[1] (numeric) = 2.0320284821895881525336662502559 absolute error = 2.0320284821895881525336662502559 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.097 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.279 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 0 y[1] (numeric) = 2.0370500702300972144444342047277 absolute error = 2.0370500702300972144444342047277 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.108 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.294 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=264079872, alloc=4521156, time=8.68 x[1] = 3.57 y[1] (analytic) = 0 y[1] (numeric) = 2.0420724599390407422750956871651 absolute error = 2.0420724599390407422750956871651 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.12 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 = 4.308 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0 y[1] (numeric) = 2.0470956791477749084257848736242 absolute error = 2.0470956791477749084257848736242 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.131 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.323 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0 y[1] (numeric) = 2.0521197555853150876791248467056 absolute error = 2.0521197555853150876791248467056 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.143 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.337 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 0 y[1] (numeric) = 2.0571447168790996526772106183316 absolute error = 2.0571447168790996526772106183316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.154 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.352 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0 y[1] (numeric) = 2.0621705905557450100071283262804 absolute error = 2.0621705905557450100071283262804 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.166 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 = 4.367 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 0 y[1] (numeric) = 2.0671974040417919766327408039698 absolute error = 2.0671974040417919766327408039698 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.177 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 = 4.381 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=268081248, alloc=4521156, time=8.81 x[1] = 3.63 y[1] (analytic) = 0 y[1] (numeric) = 2.0722251846644435949694508255197 absolute error = 2.0722251846644435949694508255197 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.189 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.396 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0 y[1] (numeric) = 2.0772539596522944834823237092392 absolute error = 2.0772539596522944834823237092392 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.201 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.41 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 0 y[1] (numeric) = 2.0822837561360518182958326367447 absolute error = 2.0822837561360518182958326367447 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.212 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.425 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0 y[1] (numeric) = 2.0873146011492480399351155405005 absolute error = 2.0873146011492480399351155405005 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.224 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.44 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0 y[1] (numeric) = 2.092346521628945377973544513876 absolute error = 2.092346521628945377973544513876 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.235 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.454 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop bytes used=272083700, alloc=4586680, time=8.94 x[1] = 3.68 y[1] (analytic) = 0 y[1] (numeric) = 2.0973795444164322850391601930456 absolute error = 2.0973795444164322850391601930456 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.247 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 = 4.469 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0 y[1] (numeric) = 2.1024136962579118703326769966515 absolute error = 2.1024136962579118703326769966515 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.258 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 = 4.483 Order of pole (six term test) = -1.033 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 0 y[1] (numeric) = 2.1074490038051824215318925556161 absolute error = 2.1074490038051824215318925556161 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.498 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0 y[1] (numeric) = 2.1124854936163101027010174796591 absolute error = 2.1124854936163101027010174796591 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.281 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.513 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0 y[1] (numeric) = 2.1175231921562939145882702105666 absolute error = 2.1175231921562939145882702105666 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.293 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.527 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 0 y[1] (numeric) = 2.1225621257977230024806553710353 absolute error = 2.1225621257977230024806553710353 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.305 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.542 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop bytes used=276085672, alloc=4586680, time=9.08 x[1] = 3.74 y[1] (analytic) = 0 y[1] (numeric) = 2.1276023208214263955907706286448 absolute error = 2.1276023208214263955907706286448 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.316 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.557 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 0 y[1] (numeric) = 2.1326438034171152607763829766758 absolute error = 2.1326438034171152607763829766758 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 = 4.571 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0 y[1] (numeric) = 2.1376865996840177522390050270006 absolute error = 2.1376865996840177522390050270006 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.339 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 = 4.586 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 0 y[1] (numeric) = 2.1427307356315065377124179784415 absolute error = 2.1427307356315065377124179784415 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 = 4.6 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0 y[1] (numeric) = 2.1477762371797190805356707617541 absolute error = 2.1477762371797190805356707617541 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 = 4.615 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop bytes used=280086776, alloc=4586680, time=9.21 x[1] = 3.79 y[1] (analytic) = 0 y[1] (numeric) = 2.1528231301601707559071825095399 absolute error = 2.1528231301601707559071825095399 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 = 4.63 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0 y[1] (numeric) = 2.157871440316360878536843458769 absolute error = 2.157871440316360878536843458769 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 = 4.644 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0 y[1] (numeric) = 2.1629211933043717178511104540271 absolute error = 2.1629211933043717178511104540271 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.397 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.659 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0 y[1] (numeric) = 2.1679724146934605758616972834944 absolute error = 2.1679724146934605758616972834944 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.409 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.674 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 0 y[1] (numeric) = 2.1730251299666450017812439950718 absolute error = 2.1730251299666450017812439950718 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.688 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 0 y[1] (numeric) = 2.1780793645212812164589967371733 absolute error = 2.1780793645212812164589967371733 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.432 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.703 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop bytes used=284087996, alloc=4586680, time=9.34 x[1] = 3.85 y[1] (analytic) = 0 y[1] (numeric) = 2.1831351436696358187157308004908 absolute error = 2.1831351436696358187157308004908 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.443 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.718 Order of pole (six term test) = -1.034 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 0 y[1] (numeric) = 2.1881924926394508446796011241805 absolute error = 2.1881924926394508446796011241805 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.455 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.732 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0 y[1] (numeric) = 2.1932514365745022502630096095736 absolute error = 2.1932514365745022502630096095736 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.466 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.747 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 0 y[1] (numeric) = 2.1983120005351518859746463631067 absolute error = 2.1983120005351518859746463631067 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.478 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.761 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0 y[1] (numeric) = 2.2033742094988930323303076998949 absolute error = 2.2033742094988930323303076998949 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.489 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.776 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop bytes used=288089096, alloc=4586680, time=9.48 x[1] = 3.9 y[1] (analytic) = 0 y[1] (numeric) = 2.2084380883608895632106384984407 absolute error = 2.2084380883608895632106384984407 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.501 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 = 4.791 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0 y[1] (numeric) = 2.2135036619345088036133171733629 absolute error = 2.2135036619345088036133171733629 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.512 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 = 4.805 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 0 y[1] (numeric) = 2.2185709549518481473611306117852 absolute error = 2.2185709549518481473611306117852 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.524 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.82 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0 y[1] (numeric) = 2.2236399920642554994556118728776 absolute error = 2.2236399920642554994556118728776 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.536 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.835 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0 y[1] (numeric) = 2.2287107978428436069081786133612 absolute error = 2.2287107978428436069081786133612 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.547 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.849 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 0 y[1] (numeric) = 2.2337833967789983410367636476867 absolute error = 2.2337833967789983410367636476867 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.559 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.864 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop bytes used=292090220, alloc=4586680, time=9.61 x[1] = 3.96 y[1] (analytic) = 0 y[1] (numeric) = 2.2388578132848809933855244721849 absolute error = 2.2388578132848809933855244721849 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.879 Order of pole (six term test) = -1.035 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 0 y[1] (numeric) = 2.2439340716939246466081146721018 absolute error = 2.2439340716939246466081146721018 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.582 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.893 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0 y[1] (numeric) = 2.2490121962613246808509604718273 absolute error = 2.2490121962613246808509604718273 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.593 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.908 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0 y[1] (numeric) = 2.2540922111645234753817786420252 absolute error = 2.2540922111645234753817786420252 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.605 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.923 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0 y[1] (numeric) = 2.2591741405036893644299705722726 absolute error = 2.2591741405036893644299705722726 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.616 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.937 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop bytes used=296091268, alloc=4586680, time=9.74 x[1] = 4.01 y[1] (analytic) = 0 y[1] (numeric) = 2.2642580083021899054393091475021 absolute error = 2.2642580083021899054393091475021 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.628 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.952 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 0 y[1] (numeric) = 2.2693438385070595171792821852501 absolute error = 2.2693438385070595171792821852501 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.64 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 = 4.967 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0 y[1] (numeric) = 2.2744316549894615444193550133131 absolute error = 2.2744316549894615444193550133131 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.651 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 = 4.981 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 0 y[1] (numeric) = 2.2795214815451448051400559715979 absolute error = 2.2795214815451448051400559715979 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.663 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.996 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0 y[1] (numeric) = 2.2846133418948946755359670528379 absolute error = 2.2846133418948946755359670528379 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.674 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.011 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 0 y[1] (numeric) = 2.2897072596849787673582164739417 absolute error = 2.2897072596849787673582164739417 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.686 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.025 Order of pole (six term test) = -1.036 TOP MAIN SOLVE Loop bytes used=300092484, alloc=4586680, time=9.88 x[1] = 4.07 y[1] (analytic) = 0 y[1] (numeric) = 2.2948032584875872514477235961661 absolute error = 2.2948032584875872514477235961661 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.697 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.04 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0 y[1] (numeric) = 2.2999013618012678806250460862902 absolute error = 2.2999013618012678806250460862902 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.709 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 = 5.055 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0 y[1] (numeric) = 2.3050015930513557644280351394732 absolute error = 2.3050015930513557644280351394732 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.72 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 = 5.069 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0 y[1] (numeric) = 2.3101039755903979475244312989507 absolute error = 2.3101039755903979475244312989507 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.732 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.084 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 0 y[1] (numeric) = 2.3152085326985728429728488818975 absolute error = 2.3152085326985728429728488818975 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.743 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.099 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop bytes used=304093444, alloc=4586680, time=10.01 x[1] = 4.12 y[1] (analytic) = 0 y[1] (numeric) = 2.3203152875841045708621227904772 absolute error = 2.3203152875841045708621227904772 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.755 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.114 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0 y[1] (numeric) = 2.3254242633836722522255525719574 absolute error = 2.3254242633836722522255525719574 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.767 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.128 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 0 y[1] (numeric) = 2.3305354831628143075030034189125 absolute error = 2.3305354831628143075030034189125 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.778 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.143 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 0 y[1] (numeric) = 2.3356489699163278082099441300238 absolute error = 2.3356489699163278082099441300238 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 = 5.158 Order of pole (six term test) = -1.037 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0 y[1] (numeric) = 2.3407647465686629298681529041078 absolute error = 2.3407647465686629298681529041078 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 = 5.172 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0 y[1] (numeric) = 2.3458828359743125536578414242872 absolute error = 2.3458828359743125536578414242872 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 = 5.187 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop bytes used=308094788, alloc=4586680, time=10.14 x[1] = 4.18 y[1] (analytic) = 0 y[1] (numeric) = 2.351003260918197063665177335166 absolute error = 2.351003260918197063665177335166 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 = 5.202 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0 y[1] (numeric) = 2.3561260441160443860224693053207 absolute error = 2.3561260441160443860224693053207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.836 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.216 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0 y[1] (numeric) = 2.3612512082147653156704647685687 absolute error = 2.3612512082147653156704647685687 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.847 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.231 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 0 y[1] (numeric) = 2.3663787757928241759131484404015 absolute error = 2.3663787757928241759131484404015 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.859 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.246 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0 y[1] (numeric) = 2.3715087693606048553849729597665 absolute error = 2.3715087693606048553849729597665 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.871 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.26 Order of pole (six term test) = -1.038 TOP MAIN SOLVE Loop bytes used=312095684, alloc=4586680, time=10.27 x[1] = 4.23 y[1] (analytic) = 0 y[1] (numeric) = 2.3766412113607722665084574577125 absolute error = 2.3766412113607722665084574577125 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.882 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.275 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 0 y[1] (numeric) = 2.3817761241686292689864141875596 absolute error = 2.3817761241686292689864141875596 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.894 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.29 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0 y[1] (numeric) = 2.3869135300924691013475689295635 absolute error = 2.3869135300924691013475689295635 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.905 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.305 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0 y[1] (numeric) = 2.3920534513739233630468916917591 absolute error = 2.3920534513739233630468916917591 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.917 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 = 5.319 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 0 y[1] (numeric) = 2.397195910188305589112416819079 absolute error = 2.397195910188305589112416819079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.928 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 = 5.334 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0 y[1] (numeric) = 2.4023409286449504588285750577982 absolute error = 2.4023409286449504588285750577982 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.349 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop bytes used=316096736, alloc=4586680, time=10.40 x[1] = 4.29 y[1] (analytic) = 0 y[1] (numeric) = 2.4074885287875486794519559229689 absolute error = 2.4074885287875486794519559229689 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.951 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.363 Order of pole (six term test) = -1.039 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 0 y[1] (numeric) = 2.4126387325944775854688408101887 absolute error = 2.4126387325944775854688408101887 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.963 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.378 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 0 y[1] (numeric) = 2.4177915619791274934246719626702 absolute error = 2.4177915619791274934246719626702 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.974 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.393 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0 y[1] (numeric) = 2.422947038790223851883728238895 absolute error = 2.422947038790223851883728238895 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.986 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.408 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0 y[1] (numeric) = 2.4281051848121452256125464712711 absolute error = 2.4281051848121452256125464712711 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.998 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 = 5.422 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop bytes used=320097644, alloc=4586680, time=10.54 x[1] = 4.34 y[1] (analytic) = 0 y[1] (numeric) = 2.4332660217652371526229401183459 absolute error = 2.4332660217652371526229401183459 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.009 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.437 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0 y[1] (numeric) = 2.4384295713061219122597101122006 absolute error = 2.4384295713061219122597101122006 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.021 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 = 5.452 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0 y[1] (numeric) = 2.4435958550280042420742036272111 absolute error = 2.4435958550280042420742036272111 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.032 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.466 Order of pole (six term test) = -1.04 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0 y[1] (numeric) = 2.4487648944609730407876443593605 absolute error = 2.4487648944609730407876443593605 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.044 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 = 5.481 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 0 y[1] (numeric) = 2.4539367110722990942175242509717 absolute error = 2.4539367110722990942175242509717 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.055 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 = 5.496 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 0 y[1] (numeric) = 2.4591113262667288606162048574563 absolute error = 2.4591113262667288606162048574563 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.067 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 = 5.511 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop bytes used=324098432, alloc=4586680, time=10.67 x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 2.4642887613867743514531221117244 absolute error = 2.4642887613867743514531221117244 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.078 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 = 5.525 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 0 y[1] (numeric) = 2.4694690377129991432605183871982 absolute error = 2.4694690377129991432605183871982 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.09 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 = 5.54 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0 y[1] (numeric) = 2.4746521764643005557573396491663 absolute error = 2.4746521764643005557573396491663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.102 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.555 Order of pole (six term test) = -1.041 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 0 y[1] (numeric) = 2.4798381987981880310667341035869 absolute error = 2.4798381987981880310667341035869 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.113 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.569 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0 y[1] (numeric) = 2.4850271258110577484493748817475 absolute error = 2.4850271258110577484493748817475 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 = 5.584 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop bytes used=328099432, alloc=4586680, time=10.80 x[1] = 4.45 y[1] (analytic) = 0 y[1] (numeric) = 2.4902189785384635085875074732817 absolute error = 2.4902189785384635085875074732817 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 = 5.599 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0 y[1] (numeric) = 2.4954137779553839210730990934048 absolute error = 2.4954137779553839210730990934048 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.148 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.614 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 0 y[1] (numeric) = 2.5006115449764859283776498818217 absolute error = 2.5006115449764859283776498818217 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.159 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.628 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 0 y[1] (numeric) = 2.5058123004563846992110243697347 absolute error = 2.5058123004563846992110243697347 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.171 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.643 Order of pole (six term test) = -1.042 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0 y[1] (numeric) = 2.5110160651898999238119872234915 absolute error = 2.5110160651898999238119872234915 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.182 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.658 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 2.516222859912308543353892668252 absolute error = 2.516222859912308543353892668252 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.194 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 = 5.673 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop bytes used=332100280, alloc=4586680, time=10.93 x[1] = 4.51 y[1] (analytic) = 0 y[1] (numeric) = 2.521432705299593945295096553935 absolute error = 2.521432705299593945295096553935 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.205 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.687 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 0 y[1] (numeric) = 2.5266456219686916561550496103283 absolute error = 2.5266456219686916561550496103283 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.217 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 = 5.702 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 0 y[1] (numeric) = 2.5318616304777315628536074000175 absolute error = 2.5318616304777315628536074000175 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.229 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.717 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0 y[1] (numeric) = 2.5370807513262766934127756278405 absolute error = 2.5370807513262766934127756278405 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.24 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 = 5.732 Order of pole (six term test) = -1.043 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 0 y[1] (numeric) = 2.5423030049555585874868190454184 absolute error = 2.5423030049555585874868190454184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.252 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.746 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop bytes used=336101240, alloc=4586680, time=11.06 x[1] = 4.56 y[1] (analytic) = 0 y[1] (numeric) = 2.5475284117487092868583198421928 absolute error = 2.5475284117487092868583198421928 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.263 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 = 5.761 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 0 y[1] (numeric) = 2.5527569920309899757143001571942 absolute error = 2.5527569920309899757143001571942 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.275 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.776 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 0 y[1] (numeric) = 2.5579887660700163001978475416047 absolute error = 2.5579887660700163001978475416047 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.286 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 = 5.791 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 0 y[1] (numeric) = 2.5632237540759803964167275335558 absolute error = 2.5632237540759803964167275335558 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.298 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.805 Order of pole (six term test) = -1.044 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 2.5684619762018696557811609491741 absolute error = 2.5684619762018696557811609491741 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.309 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 = 5.82 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 0 y[1] (numeric) = 2.5737034525436822562382132907552 absolute error = 2.5737034525436822562382132907552 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.321 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.835 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop bytes used=340102236, alloc=4586680, time=11.20 x[1] = 4.62 y[1] (analytic) = 0 y[1] (numeric) = 2.5789482031406394876700193095707 absolute error = 2.5789482031406394876700193095707 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.332 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 = 5.85 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 0 y[1] (numeric) = 2.5841962479753948994272779404126 absolute error = 2.5841962479753948994272779404126 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.344 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.864 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 0 y[1] (numeric) = 2.5894476069742402976780334445207 absolute error = 2.5894476069742402976780334445207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.356 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 = 5.879 Order of pole (six term test) = -1.045 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 0 y[1] (numeric) = 2.594702300007308619964640724175 absolute error = 2.594702300007308619964640724175 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.367 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.894 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 0 y[1] (numeric) = 2.5999603468887737140789306203448 absolute error = 2.5999603468887737140789306203448 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.379 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 = 5.909 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop bytes used=344103624, alloc=4586680, time=11.33 x[1] = 4.67 y[1] (analytic) = 0 y[1] (numeric) = 2.6052217673770470480868799133968 absolute error = 2.6052217673770470480868799133968 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.923 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 0 y[1] (numeric) = 2.610486581174971378059487157673 absolute error = 2.610486581174971378059487157673 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 = 5.938 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 0 y[1] (numeric) = 2.6157548079300113997959969165161 absolute error = 2.6157548079300113997959969165161 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 = 5.953 Order of pole (six term test) = -1.046 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 0 y[1] (numeric) = 2.6210264672344414105590400078029 absolute error = 2.6210264672344414105590400078029 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.425 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 = 5.968 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 0 y[1] (numeric) = 2.6263015786255300065786056433251 absolute error = 2.6263015786255300065786056433251 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.436 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 = 5.982 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 0 y[1] (numeric) = 2.6315801615857218418229734896429 absolute error = 2.6315801615857218418229734896429 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.448 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 = 5.997 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop bytes used=348104560, alloc=4586680, time=11.46 x[1] = 4.73 y[1] (analytic) = 0 y[1] (numeric) = 2.6368622355428164732797513338834 absolute error = 2.6368622355428164732797513338834 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.459 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.012 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 0 y[1] (numeric) = 2.6421478198701443177389298259013 absolute error = 2.6421478198701443177389298259013 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.471 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 = 6.027 Order of pole (six term test) = -1.047 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 0 y[1] (numeric) = 2.6474369338867397448223232698401 absolute error = 2.6474369338867397448223232698401 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.483 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 = 6.041 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 0 y[1] (numeric) = 2.6527295968575113307598591774914 absolute error = 2.6527295968575113307598591774914 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.494 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 = 6.056 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 0 y[1] (numeric) = 2.6580258279934092971728547213454 absolute error = 2.6580258279934092971728547213454 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.506 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 = 6.071 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop bytes used=352105396, alloc=4586680, time=11.59 x[1] = 4.78 y[1] (analytic) = 0 y[1] (numeric) = 2.6633256464515901588876216918084 absolute error = 2.6633256464515901588876216918084 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.517 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 = 6.086 Order of pole (six term test) = -1.048 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 0 y[1] (numeric) = 2.6686290713355786045694203148449 absolute error = 2.6686290713355786045694203148449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.529 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 = 6.1 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 0 y[1] (numeric) = 2.6739361216954266337368844395146 absolute error = 2.6739361216954266337368844395146 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.54 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 = 6.115 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 0 y[1] (numeric) = 2.6792468165278699734905151311958 absolute error = 2.6792468165278699734905151311958 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.552 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.13 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 0 y[1] (numeric) = 2.6845611747764817980656364165011 absolute error = 2.6845611747764817980656364165011 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.563 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.145 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 0 y[1] (numeric) = 2.6898792153318237741002764539225 absolute error = 2.6898792153318237741002764539225 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.575 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 = 6.16 Order of pole (six term test) = -1.049 TOP MAIN SOLVE Loop bytes used=356107568, alloc=4586680, time=11.72 x[1] = 4.84 y[1] (analytic) = 0 y[1] (numeric) = 2.6952009570315944542917311914644 absolute error = 2.6952009570315944542917311914644 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.586 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.174 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 0 y[1] (numeric) = 2.7005264186607750419020378524647 absolute error = 2.7005264186607750419020378524647 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.598 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 = 6.189 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 0 y[1] (numeric) = 2.7058556189517725483621853741132 absolute error = 2.7058556189517725483621853741132 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.204 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 0 y[1] (numeric) = 2.7111885765845603660175719829228 absolute error = 2.7111885765845603660175719829228 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.621 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 = 6.219 Order of pole (six term test) = -1.05 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 0 y[1] (numeric) = 2.7165253101868162778529409486979 absolute error = 2.7165253101868162778529409486979 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 = 6.234 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop bytes used=360108668, alloc=4586680, time=11.85 x[1] = 4.89 y[1] (analytic) = 0 y[1] (numeric) = 2.721865838334057925833739468404 absolute error = 2.721865838334057925833739468404 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 = 6.248 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 0 y[1] (numeric) = 2.7272101795497757593025085689128 absolute error = 2.7272101795497757593025085689128 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.656 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 = 6.263 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 0 y[1] (numeric) = 2.7325583523055634846734805646223 absolute error = 2.7325583523055634846734805646223 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.667 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 = 6.278 Order of pole (six term test) = -1.051 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 0 y[1] (numeric) = 2.7379103750212460374759923375035 absolute error = 2.7379103750212460374759923375035 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.679 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.293 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 0 y[1] (numeric) = 2.7432662660650050976075755786543 absolute error = 2.7432662660650050976075755786543 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.69 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 = 6.308 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 0 y[1] (numeric) = 2.7486260437535021684706178650415 absolute error = 2.7486260437535021684706178650415 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.702 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.322 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop bytes used=364109648, alloc=4586680, time=11.99 x[1] = 4.95 y[1] (analytic) = 0 y[1] (numeric) = 2.7539897263519992404822604210873 absolute error = 2.7539897263519992404822604210873 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.713 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 = 6.337 Order of pole (six term test) = -1.052 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 0 y[1] (numeric) = 2.7593573320744770592656696534102 absolute error = 2.7593573320744770592656696534102 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.725 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.352 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 0 y[1] (numeric) = 2.7647288790837510186519507007147 absolute error = 2.7647288790837510186519507007147 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.737 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.367 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 0 y[1] (numeric) = 2.7701043854915846984457235812509 absolute error = 2.7701043854915846984457235812509 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.748 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.382 Order of pole (six term test) = -1.053 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 0 y[1] (numeric) = 2.7754838693588010667337179269977 absolute error = 2.7754838693588010667337179269977 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 5.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.396 Order of pole (six term test) = -1.053 Finished! diff ( y , x , 1 ) = expt(sin(0.1 * x) , sin(0.2 * x)); Iterations = 490 Total Elapsed Time = 12 Seconds Elapsed Time(since restart) = 11 Seconds Time to Timeout = 2 Minutes 47 Seconds Percent Done = 100.2 % > quit bytes used=367646408, alloc=4586680, time=12.09