##############ECHO OF PROBLEM################# ##############temp/mtest6_rev_sm_hpostode.ode################# diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ /* # problem from Boyce DePrima - */ /* # _Elementary Differential Equations and Boundary Value Problems_ */ /* # page 269 */ /* # */ t_start=0.5; t_end=0.8; array_x1_init[0 + 1] = exact_soln_x1(t_start); /* # I think following line should be omitted */ /* # diff(x1,1,exact_soln_x1p(t_start)); */ array_x2_init[0 + 1] = exact_soln_x2(t_start); array_x2_init[1 + 1] = exact_soln_x2p(t_start); glob_max_h=0.0001; 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_x1 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)); } double exact_soln_x1p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( - 6.0 * c3 * exp(-t)); } double exact_soln_x2 (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); } double exact_soln_x2p (double t) { double c1,c2,c3; c1 = 1.0; c2 = 0.0002; c3 = 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); } /* 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 = 0.3 estimated_steps = 300000.0000000001 step_error = 3.333333333333333e-16 est_needed_step_err = 3.333333333333333e-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 = 2.115801377437765e-178 estimated_step_error = 2.115801377437765e-178 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 = 1.419890321483369e-170 estimated_step_error = 1.419890321483369e-170 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 = 9.528723353765782e-163 estimated_step_error = 9.528723353765782e-163 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 = 6.394618943766007e-155 estimated_step_error = 6.394618943766007e-155 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 = 4.291357401803819e-147 estimated_step_error = 4.291357401803819e-147 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 = 2.879882909128657e-139 estimated_step_error = 2.879882909128657e-139 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 = 1.932658995407649e-131 estimated_step_error = 1.932658995407649e-131 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 = 1.296988571161701e-123 estimated_step_error = 1.296988571161701e-123 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop t[1] = 0.5 x2[1] (analytic) = 1.000725615563606 x2[1] (numeric) = 1.000725615563606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 x1[1] (analytic) = 2.001091755187483 x1[1] (numeric) = 2.001091755187483 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.5 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 504.4 Order of pole (six term test) = 5.21e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.600099999999989 x2[1] (analytic) = 1.000828783229808 x2[1] (numeric) = 1.000835025949199 absolute error = 6.242719390758822e-06 relative error = 0.0006237549814077822 % Correct digits = 6 h = 0.0001 x1[1] (analytic) = 2.000987762163814 x1[1] (numeric) = 2.000976813628459 absolute error = 1.094853535432705e-05 relative error = 0.0005471565374536624 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.5 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 530.3 Order of pole (six term test) = 5.759e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop t[1] = 0.700099999999978 x2[1] (analytic) = 1.000960162911913 x2[1] (numeric) = 1.000988570262652 absolute error = 2.840735073927902e-05 relative error = 0.002838010121865255 % Correct digits = 5 h = 0.0001 x1[1] (analytic) = 2.000893764165939 x1[1] (numeric) = 2.000849904223788 absolute error = 4.385994215150291e-05 relative error = 0.00219201753421355 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.5 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 557.5 Order of pole (six term test) = 6.365e+07 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1; diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1; Iterations = 3001 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100.1 %