##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.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=0.2; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.5; glob_type_given_pole=4; array_given_rad_poles[1][1]=0.5; 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=1000000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(2.0/(1.0 - 2.0*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 = 0.2 estimated_steps = 200000 step_error = 4.999999999999999e-16 est_needed_step_err = 4.999999999999999e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.310721310721311e-91 estimated_step_error = 1.310721310721311e-91 best_h = 2e-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 = 8.589951771903542e-87 estimated_step_error = 8.589951771903542e-87 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.629522052301328e-82 estimated_step_error = 5.629522052301328e-82 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.689378329768548e-77 estimated_step_error = 3.689378329768548e-77 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.417890325474466e-72 estimated_step_error = 2.417890325474466e-72 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.584613957931941e-67 estimated_step_error = 1.584613957931941e-67 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.038525837360556e-62 estimated_step_error = 1.038525837360556e-62 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 = 6.806518572796085e-58 estimated_step_error = 6.806518572796085e-58 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.461291130235445e-53 estimated_step_error = 4.461291130235445e-53 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.924500618978521e-48 estimated_step_error = 2.924500618978521e-48 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 = 1.917583031104105e-43 estimated_step_error = 1.917583031104105e-43 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.257996724346713e-38 estimated_step_error = 1.257996724346713e-38 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 = 8.261361320257963e-34 estimated_step_error = 8.261361320257963e-34 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 = 5.436525324605938e-29 estimated_step_error = 5.436525324605938e-29 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 = 3.592554284321596e-24 estimated_step_error = 3.592554284321596e-24 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.394295385969994e-19 estimated_step_error = 2.394295385969994e-19 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.624120431864762e-14 estimated_step_error = 1.624120431864762e-14 best_h = 0.032768 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.5 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) = 2.040816326530612 y[1] (numeric) = 2.040816326530612 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.49 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.49 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.49 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) = 2.083333333333333 y[1] (numeric) = 2.083333333333333 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.48 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.48 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.48 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) = 2.127659574468085 y[1] (numeric) = 2.127659574468085 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.47 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.47 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.47 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) = 2.173913043478261 y[1] (numeric) = 2.173913043478261 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.46 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.46 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.46 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) = 2.222222222222222 y[1] (numeric) = 2.222222222222222 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.45 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.45 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.45 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) = 2.272727272727273 y[1] (numeric) = 2.272727272727273 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.44 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.44 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.44 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) = 2.325581395348837 y[1] (numeric) = 2.325581395348837 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.43 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.43 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.43 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) = 2.380952380952381 y[1] (numeric) = 2.380952380952381 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.42 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.42 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.42 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) = 2.439024390243902 y[1] (numeric) = 2.439024390243902 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.41 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.41 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.41 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) = 2.5 y[1] (numeric) = 2.5 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.4 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.4 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) = 2.564102564102564 y[1] (numeric) = 2.564102564102564 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.39 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.39 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.39 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) = 2.631578947368421 y[1] (numeric) = 2.631578947368421 absolute error = 4.440892098500626e-16 relative error = 1.687538997430238e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.38 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.38 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.38 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) = 2.702702702702703 y[1] (numeric) = 2.702702702702703 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.37 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.37 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.37 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) = 2.777777777777778 y[1] (numeric) = 2.777777777777778 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.36 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.36 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.36 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) = 2.857142857142857 y[1] (numeric) = 2.857142857142857 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.35 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.35 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.35 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) = 2.941176470588236 y[1] (numeric) = 2.941176470588236 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.34 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.34 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.34 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) = 3.030303030303031 y[1] (numeric) = 3.030303030303031 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.33 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.33 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.33 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) = 3.125 y[1] (numeric) = 3.125 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.32 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.32 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.32 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) = 3.225806451612904 y[1] (numeric) = 3.225806451612904 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.31 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.31 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations = 20 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 105 %