##############ECHO OF PROBLEM################# ##############temp/lin_tanpostode.ode################# diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=0.1; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10; // # Not Given = 0 // # No Pole = 3 // # Pole = 4 glob_type_given_pole=4; // # Real Part array_given_rad_poles[1][1]=0.8561944; // # Imag Part array_given_rad_poles[1][2]=0.0; // # Order array_given_ord_poles[1][1]=0.0; // # Not Used 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=30.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(ln(1.0 + expt(tan(2.0 * x + 3.0),2))/4.0); } // 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 = 0.1 estimated_steps = 100000 step_error = 9.999999999999999e-16 est_needed_step_err = 9.999999999999999e-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 = 1.208539714631239e-154 estimated_step_error = 1.208539714631239e-154 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 = 8.110367360568399e-147 estimated_step_error = 8.110367360568399e-147 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 = 5.442768188776129e-139 estimated_step_error = 5.442768188776129e-139 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 = 3.652570220384113e-131 estimated_step_error = 3.652570220384113e-131 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 = 2.451185387845672e-123 estimated_step_error = 2.451185387845672e-123 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 = 1.644945228544742e-115 estimated_step_error = 1.644945228544742e-115 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 = 1.10388064980085e-107 estimated_step_error = 1.10388064980085e-107 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.407703503909264e-100 estimated_step_error = 7.407703503909264e-100 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 = 4.970804099051622e-92 estimated_step_error = 4.970804099051622e-92 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.335284488245168e-84 estimated_step_error = 3.335284488245168e-84 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.237512694710478e-76 estimated_step_error = 2.237512694710478e-76 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 = 1.500551927019545e-68 estimated_step_error = 1.500551927019545e-68 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.005640650597852e-60 estimated_step_error = 1.005640650597852e-60 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.730526763910631e-53 estimated_step_error = 6.730526763910631e-53 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.492537718066949e-45 estimated_step_error = 4.492537718066949e-45 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 = 2.982888539048538e-37 estimated_step_error = 2.982888539048538e-37 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 = 1.960208604997565e-29 estimated_step_error = 1.960208604997565e-29 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.263068769601934e-21 estimated_step_error = 1.263068769601934e-21 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 0.005028957536846423 y[1] (numeric) = 0.005028957536846423 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8562 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 0.003705337319408968 y[1] (numeric) = 0.003705337319408919 absolute error = 4.85722573273506e-17 relative error = 1.310872753012897e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 0.8462 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 0.002584717588216024 y[1] (numeric) = 0.002584717588216025 absolute error = 8.673617379884035e-19 relative error = 3.355731171338754e-14 % Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8362 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 0.001666190250721918 y[1] (numeric) = 0.001666190250721898 absolute error = 2.016616040823038e-17 relative error = 1.210315592681742e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 0.8262 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 0.0009490140104840613 y[1] (numeric) = 0.0009490140104840653 absolute error = 4.011548038196366e-18 relative error = 4.227069351853094e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.8162 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 0.0004326119625055668 y[1] (numeric) = 0.0004326119625055726 absolute error = 5.746271514173174e-18 relative error = 1.328273837110834e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 0.8062 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02548 Order of pole (three term test) = 21.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 0.0001165697309820659 y[1] (numeric) = 0.0001165697309820295 absolute error = 3.637498288688867e-17 relative error = 3.120448385737882e-11 % Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 0.7962 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01143 Order of pole (three term test) = 21.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000001 y[1] (analytic) = 6.341366323577824e-07 y[1] (numeric) = 6.341366323363122e-07 absolute error = 2.147016763052838e-17 relative error = 3.385732117493383e-09 % Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.7862 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0007966 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 8.47123844836277e-05 y[1] (numeric) = 8.471238448363442e-05 absolute error = 6.722053469410127e-18 relative error = 7.935148456019786e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 0.7762 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009594 Order of pole (three term test) = 21.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 0.0003688717665651817 y[1] (numeric) = 0.000368871766565178 absolute error = 3.63207727782644e-18 relative error = 9.846449652808089e-13 % Correct digits = 15 h = 0.01 Radius of convergence (given) for eq 1 = 0.7662 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02287 Order of pole (three term test) = 21.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999999 y[1] (analytic) = 0.0008533398774849093 y[1] (numeric) = 0.0008533398774848628 absolute error = 4.651227319962814e-17 relative error = 5.450615215207809e-12 % Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 0.7562 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; Iterations = 11 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 30 Minutes 0.0 Seconds Percent Done = 120 %