##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=1.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.0; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(1.0/(1.0 - x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 500000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.00000050000025e-96 estimated_step_error = 1.00000050000025e-96 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 250000 step_error = 1e-14 est_needed_step_err = 1e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.553606553606554e-92 estimated_step_error = 6.553606553606554e-92 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 125000 step_error = 1.414213562373095e-14 est_needed_step_err = 1.414213562373095e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.294975885951771e-87 estimated_step_error = 4.294975885951771e-87 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 62500 step_error = 2e-14 est_needed_step_err = 2e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.814761026150664e-82 estimated_step_error = 2.814761026150664e-82 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 31250 step_error = 2.82842712474619e-14 est_needed_step_err = 2.82842712474619e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.844689164884274e-77 estimated_step_error = 1.844689164884274e-77 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 15625 step_error = 4e-14 est_needed_step_err = 4e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.208945162737233e-72 estimated_step_error = 1.208945162737233e-72 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 7812.5 step_error = 5.65685424949238e-14 est_needed_step_err = 5.65685424949238e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.923069789659704e-68 estimated_step_error = 7.923069789659704e-68 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 3906.25 step_error = 8e-14 est_needed_step_err = 8e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.192629186802782e-63 estimated_step_error = 5.192629186802782e-63 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 1953.125 step_error = 1.131370849898476e-13 est_needed_step_err = 1.131370849898476e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.403259286398042e-58 estimated_step_error = 3.403259286398042e-58 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 976.5625 step_error = 1.6e-13 est_needed_step_err = 1.6e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.230645565117723e-53 estimated_step_error = 2.230645565117723e-53 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 488.28125 step_error = 2.262741699796952e-13 est_needed_step_err = 2.262741699796952e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.462250309489261e-48 estimated_step_error = 1.462250309489261e-48 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 244.140625 step_error = 3.2e-13 est_needed_step_err = 3.2e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.587915155520526e-44 estimated_step_error = 9.587915155520526e-44 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 122.0703125 step_error = 4.525483399593904e-13 est_needed_step_err = 4.525483399593904e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.289983621733564e-39 estimated_step_error = 6.289983621733564e-39 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.5 estimated_steps = 61.03515625 step_error = 6.4e-13 est_needed_step_err = 6.4e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.130680660128981e-34 estimated_step_error = 4.130680660128981e-34 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6104 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6104 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 1.01010101010101 y[1] (numeric) = 1.01010101010101 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.99 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 1.020408163265306 y[1] (numeric) = 1.020408163265306 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.98 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 1.030927835051547 y[1] (numeric) = 1.030927835051547 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.97 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 1.041666666666667 y[1] (numeric) = 1.041666666666667 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.96 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 1.052631578947368 y[1] (numeric) = 1.052631578947369 absolute error = 2.220446049250313e-16 relative error = 2.109423746787797e-14 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.95 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 1.063829787234043 y[1] (numeric) = 1.063829787234043 absolute error = 2.220446049250313e-16 relative error = 2.087219286295294e-14 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.94 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000001 y[1] (analytic) = 1.075268817204301 y[1] (numeric) = 1.075268817204301 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.93 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 1.08695652173913 y[1] (numeric) = 1.086956521739131 absolute error = 2.220446049250313e-16 relative error = 2.042810365310288e-14 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.92 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 1.098901098901099 y[1] (numeric) = 1.098901098901099 absolute error = 2.220446049250313e-16 relative error = 2.020605904817785e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.91 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999999 y[1] (analytic) = 1.111111111111111 y[1] (numeric) = 1.111111111111111 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.123595505617978 y[1] (numeric) = 1.123595505617978 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.89 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.136363636363636 y[1] (numeric) = 1.136363636363636 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.88 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.149425287356322 y[1] (numeric) = 1.149425287356322 absolute error = 2.220446049250313e-16 relative error = 1.931788062847772e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.87 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.162790697674419 y[1] (numeric) = 1.162790697674419 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.86 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.176470588235294 y[1] (numeric) = 1.176470588235294 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.85 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.19047619047619 y[1] (numeric) = 1.19047619047619 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.84 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.204819277108434 y[1] (numeric) = 1.204819277108434 absolute error = 2.220446049250313e-16 relative error = 1.84297022087776e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.83 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 1.219512195121951 y[1] (numeric) = 1.219512195121951 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.82 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 1.234567901234568 y[1] (numeric) = 1.234567901234568 absolute error = 2.220446049250313e-16 relative error = 1.798561299892753e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.81 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.25 y[1] (numeric) = 1.25 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 1.265822784810127 y[1] (numeric) = 1.265822784810127 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.79 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 1.282051282051282 y[1] (numeric) = 1.282051282051282 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.78 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 1.298701298701299 y[1] (numeric) = 1.298701298701299 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.77 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 1.315789473684211 y[1] (numeric) = 1.315789473684211 absolute error = 2.220446049250313e-16 relative error = 1.687538997430238e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.76 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 1.333333333333333 y[1] (numeric) = 1.333333333333334 absolute error = 4.440892098500626e-16 relative error = 3.33066907387547e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.75 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (analytic) = 1.351351351351351 y[1] (numeric) = 1.351351351351352 absolute error = 4.440892098500626e-16 relative error = 3.286260152890463e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.74 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (analytic) = 1.36986301369863 y[1] (numeric) = 1.369863013698631 absolute error = 4.440892098500626e-16 relative error = 3.241851231905457e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.73 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 1.388888888888889 y[1] (numeric) = 1.388888888888889 absolute error = 4.440892098500626e-16 relative error = 3.197442310920451e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.72 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 1.408450704225352 y[1] (numeric) = 1.408450704225352 absolute error = 2.220446049250313e-16 relative error = 1.576516694967722e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.71 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (analytic) = 1.428571428571429 y[1] (numeric) = 1.428571428571429 absolute error = 2.220446049250313e-16 relative error = 1.554312234475219e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y[1] (analytic) = 1.449275362318841 y[1] (numeric) = 1.449275362318841 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.69 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.69 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.69 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (analytic) = 1.470588235294118 y[1] (numeric) = 1.470588235294118 absolute error = 2.220446049250313e-16 relative error = 1.509903313490213e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.68 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.68 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.68 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (analytic) = 1.492537313432836 y[1] (numeric) = 1.492537313432836 absolute error = 2.220446049250313e-16 relative error = 1.48769885299771e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.67 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.67 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.67 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (analytic) = 1.515151515151515 y[1] (numeric) = 1.515151515151516 absolute error = 2.220446049250313e-16 relative error = 1.465494392505206e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.66 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.66 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.66 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y[1] (analytic) = 1.538461538461539 y[1] (numeric) = 1.538461538461539 absolute error = 2.220446049250313e-16 relative error = 1.443289932012703e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.65 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.65 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.65 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 1.5625 y[1] (numeric) = 1.5625 absolute error = 2.220446049250313e-16 relative error = 1.4210854715202e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.64 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.64 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.64 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 1.587301587301588 y[1] (numeric) = 1.587301587301588 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.63 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.63 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.63 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 1.612903225806452 y[1] (numeric) = 1.612903225806452 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.62 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.62 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.62 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (analytic) = 1.639344262295082 y[1] (numeric) = 1.639344262295082 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.61 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.61 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.61 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 1.666666666666667 y[1] (numeric) = 1.666666666666667 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y[1] (analytic) = 1.694915254237289 y[1] (numeric) = 1.694915254237289 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.59 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.59 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.59 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (analytic) = 1.724137931034483 y[1] (numeric) = 1.724137931034483 absolute error = 2.220446049250313e-16 relative error = 1.287858708565181e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.58 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.58 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.58 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y[1] (analytic) = 1.754385964912281 y[1] (numeric) = 1.754385964912281 absolute error = 2.220446049250313e-16 relative error = 1.265654248072678e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.57 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.57 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.57 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (analytic) = 1.785714285714286 y[1] (numeric) = 1.785714285714286 absolute error = 2.220446049250313e-16 relative error = 1.243449787580175e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.56 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.56 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.56 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (analytic) = 1.818181818181819 y[1] (numeric) = 1.818181818181819 absolute error = 2.220446049250313e-16 relative error = 1.221245327087672e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.55 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.55 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.55 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y[1] (analytic) = 1.851851851851853 y[1] (numeric) = 1.851851851851852 absolute error = 2.220446049250313e-16 relative error = 1.199040866595169e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.54 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.54 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.54 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 1.886792452830189 y[1] (numeric) = 1.886792452830189 absolute error = 2.220446049250313e-16 relative error = 1.176836406102665e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.53 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.53 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.53 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 1.923076923076924 y[1] (numeric) = 1.923076923076924 absolute error = 2.220446049250313e-16 relative error = 1.154631945610162e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.52 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.52 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.52 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 1.960784313725491 y[1] (numeric) = 1.960784313725491 absolute error = 2.220446049250313e-16 relative error = 1.132427485117659e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.51 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.51 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.51 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %