##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=1.1; x_end=2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(ln(cosh(3.0*x + 1.0))/3.0); } /* 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 = 1e-10 range = 0.8999999999999999 estimated_steps = 900000 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-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 = 4.114948349378717e-163 estimated_step_error = 4.114948349378717e-163 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 = 2.761494174506531e-155 estimated_step_error = 2.761494174506531e-155 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 = 1.853206139231448e-147 estimated_step_error = 1.853206139231448e-147 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 = 1.243663935793676e-139 estimated_step_error = 1.243663935793676e-139 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 = 8.346065222575855e-132 estimated_step_error = 8.346065222575855e-132 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 = 5.600919803289607e-124 estimated_step_error = 5.600919803289607e-124 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 = 3.758673715897868e-116 estimated_step_error = 3.758673715897868e-116 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 = 2.522349630320909e-108 estimated_step_error = 2.522349630320909e-108 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 = 1.69264824383644e-100 estimated_step_error = 1.69264824383644e-100 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 = 1.135820463697788e-92 estimated_step_error = 1.135820463697788e-92 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 = 7.621066599549855e-85 estimated_step_error = 7.621066599549855e-85 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 = 5.112673208506e-77 estimated_step_error = 5.112673208506e-77 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 = 3.428726294985577e-69 estimated_step_error = 3.428726294985577e-69 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 = 2.297856814663102e-61 estimated_step_error = 2.297856814663102e-61 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 = 1.537889880465241e-53 estimated_step_error = 1.537889880465241e-53 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 = 1.026496559283106e-45 estimated_step_error = 1.026496559283106e-45 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 = 6.815117159449936e-38 estimated_step_error = 6.815117159449936e-38 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 = 4.477716319818289e-30 estimated_step_error = 4.477716319818289e-30 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 1.20234563609611 y[1] (numeric) = 1.20234563609611 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.338 Order of pole (six term test) = -0.0304 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.302317951245919 y[1] (numeric) = 1.302317951245919 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.3 Order of pole (six term test) = 0.04161 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.402302756500702 y[1] (numeric) = 1.402302756500702 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.315 Order of pole (six term test) = 0.7714 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.502294417153335 y[1] (numeric) = 1.502294417153335 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.327 Order of pole (six term test) = 2.15 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 1.602289840333792 y[1] (numeric) = 1.602289840333792 absolute error = 2.220446049250313e-16 relative error = 1.38579549926357e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.309 Order of pole (six term test) = 2.924 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (analytic) = 1.702287328495261 y[1] (numeric) = 1.702287328495261 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.267 Order of pole (six term test) = 2.006 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (analytic) = 1.802285949961004 y[1] (numeric) = 1.802285949961004 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.218 Order of pole (six term test) = 0.5485 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (analytic) = 1.902285193402939 y[1] (numeric) = 1.902285193402939 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.162 Order of pole (six term test) = 0.1144 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 2.002284778194341 y[1] (numeric) = 2.00228477819434 absolute error = 4.440892098500626e-16 relative error = 2.217912330385601e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.101 Order of pole (six term test) = 0.671 Finished! diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; Iterations = 9 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 111.1 %