##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; /* 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(sinh(2.0*x+3.0)/2); } /* 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 = 1.9 estimated_steps = 1900000 step_error = 5.263157894736842e-17 est_needed_step_err = 5.263157894736842e-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 = 1.018875196180601e-174 estimated_step_error = 1.018875196180601e-174 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 = 6.837555443259931e-167 estimated_step_error = 6.837555443259931e-167 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 = 4.588605442313687e-159 estimated_step_error = 4.588605442313687e-159 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 = 3.079360528058466e-151 estimated_step_error = 3.079360528058466e-151 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 = 2.066523254502221e-143 estimated_step_error = 2.066523254502221e-143 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 = 1.386819455835399e-135 estimated_step_error = 1.386819455835399e-135 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 = 9.306776758387305e-128 estimated_step_error = 9.306776758387305e-128 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 = 6.245657303597561e-120 estimated_step_error = 6.245657303597561e-120 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 = 4.191369728977114e-112 estimated_step_error = 4.191369728977114e-112 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 = 2.812753852070349e-104 estimated_step_error = 2.812753852070349e-104 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 = 1.887571240821481e-96 estimated_step_error = 1.887571240821481e-96 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 = 1.266679408068671e-88 estimated_step_error = 1.266679408068671e-88 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 = 8.499894493959359e-81 estimated_step_error = 8.499894493959359e-81 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 = 5.703313898021663e-73 estimated_step_error = 5.703313898021663e-73 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 = 3.826262657025561e-65 estimated_step_error = 3.826262657025561e-65 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 = 2.566194370727617e-57 estimated_step_error = 2.566194370727617e-57 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 = 1.72003698199871e-49 estimated_step_error = 1.72003698199871e-49 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 = 1.151459573928655e-41 estimated_step_error = 1.151459573928655e-41 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 6.122941998282746 y[1] (numeric) = 6.122941998282746 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 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 7.482681694359171 y[1] (numeric) = 7.482681662377469 absolute error = 3.198170261953237e-08 relative error = 4.274096363559313e-07 % Correct digits = 9 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 9.142727680307674 y[1] (numeric) = 9.142727609283751 absolute error = 7.102392274305203e-08 relative error = 7.768351549617838e-07 % Correct digits = 9 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 11.16970343036116 y[1] (numeric) = 11.16970331166761 absolute error = 1.186935563168845e-07 relative error = 1.062638386568574e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 13.64495859856387 y[1] (numeric) = 13.64495842166011 absolute error = 1.769037609733459e-07 relative error = 1.296477081227384e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 16.66783386602617 y[1] (numeric) = 16.66783361803546 absolute error = 2.479907124097736e-07 relative error = 1.487840078099469e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 20.35964783126627 y[1] (numeric) = 20.35964749645889 absolute error = 3.348073818187913e-07 relative error = 1.644465486798e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 24.86856595154729 y[1] (numeric) = 24.86856551070928 absolute error = 4.408380043230409e-07 relative error = 1.772671593456367e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 30.37554694292146 y[1] (numeric) = 30.37554637258346 absolute error = 5.70338002603421e-07 relative error = 1.877622166524739e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 37.10160528889438 y[1] (numeric) = 37.10160456038973 absolute error = 7.285046450533628e-07 relative error = 1.963539419334575e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 45.31668132768257 y[1] (numeric) = 45.31668040599689 absolute error = 9.216856824423303e-07 relative error = 2.033877273089944e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 55.35047490581114 y[1] (numeric) = 55.35047374817687 absolute error = 1.157634265780416e-06 relative error = 2.091462210126183e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 67.60567739060902 y[1] (numeric) = 67.60567594478937 absolute error = 1.445819648893121e-06 relative error = 2.138606851817384e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 82.57413308872589 y[1] (numeric) = 82.57413129091792 absolute error = 1.797807968273446e-06 relative error = 2.177204774698272e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 100.8565786851396 y[1] (numeric) = 100.8565764574142 absolute error = 2.227725431680483e-06 relative error = 2.208805276485866e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 123.1867529156551 y[1] (numeric) = 123.1867501628286 absolute error = 2.752826532059771e-06 relative error = 2.234677403945055e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 150.4608440787023 y[1] (numeric) = 150.4608406845173 absolute error = 3.394184943772416e-06 relative error = 2.255859299843489e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 183.7734572184841 y[1] (numeric) = 183.7734530409429 absolute error = 4.177541228500559e-06 relative error = 2.273201631905948e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 224.4615444688176 y[1] (numeric) = 224.4615393344841 absolute error = 5.134333548539871e-06 relative error = 2.287400080352355e-06 % Correct digits = 8 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.25 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ; Iterations = 19 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 105.3 %