##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=0.5; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_max_iter=20; /* 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_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 - sin(x)); } /* 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 = 0.4 estimated_steps = 400000.0000000001 step_error = 2.5e-16 est_needed_step_err = 2.5e-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 = 2.467208605532302e-183 estimated_step_error = 2.467208605532302e-183 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 = 1.655715664606566e-175 estimated_step_error = 1.655715664606566e-175 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 = 1.111131969458436e-167 estimated_step_error = 1.111131969458436e-167 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 = 7.456680367024186e-160 estimated_step_error = 7.456680367024186e-160 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 = 5.004093412037816e-152 estimated_step_error = 5.004093412037816e-152 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 = 3.358190142481624e-144 estimated_step_error = 3.358190142481624e-144 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 = 2.25364312158092e-136 estimated_step_error = 2.25364312158092e-136 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 = 1.512394117654307e-128 estimated_step_error = 1.512394117654307e-128 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 = 1.014950270158055e-120 estimated_step_error = 1.014950270158055e-120 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 = 6.811212724408107e-113 estimated_step_error = 6.811212724408107e-113 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 = 4.570923134360025e-105 estimated_step_error = 4.570923134360025e-105 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 = 3.067488750234022e-97 estimated_step_error = 3.067488750234022e-97 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 = 2.05854901161809e-89 estimated_step_error = 2.05854901161809e-89 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 = 1.381458319740244e-81 estimated_step_error = 1.381458319740244e-81 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 = 9.270668118428105e-74 estimated_step_error = 9.270668118428105e-74 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 = 6.221249002016115e-66 estimated_step_error = 6.221249002016115e-66 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 = 4.174750875079241e-58 estimated_step_error = 4.174750875079241e-58 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 = 2.801274754399603e-50 estimated_step_error = 2.801274754399603e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 0.9001665833531718 y2[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 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 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2 y2[1] (analytic) = 0.8013306692049388 y2[1] (numeric) = 0.8013306692049387 absolute error = 1.110223024625157e-16 relative error = 1.38547427084838e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066577841242 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 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3 y2[1] (analytic) = 0.7044797933386604 y2[1] (numeric) = 0.7044797933386603 absolute error = 1.110223024625157e-16 relative error = 1.575947294901964e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955336489125606 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 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4 y2[1] (analytic) = 0.6105816576913494 y2[1] (numeric) = 0.6105816576913494 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921060994002885 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 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; Iterations = 4 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 125 %