##############ECHO OF PROBLEM################# ##############temp/mtest7_sm_hpostode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.0; x_end=0.5; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[4 + 1] = exact_soln_y2pppp(x_start); glob_look_poles=true; glob_max_iter=20; glob_max_h=0.0001; /* 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( cos(x)); } double exact_soln_y2 (double x) { return( sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } double exact_soln_y2pppp (double x) { return( 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 = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-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 = 2.479596263224795e-183 estimated_step_error = 2.479596263224795e-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 = 1.66402888403661e-175 estimated_step_error = 1.66402888403661e-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 = 1.116710880708846e-167 estimated_step_error = 1.116710880708846e-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 = 7.494119862081017e-160 estimated_step_error = 7.494119862081017e-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 = 5.029218706240937e-152 estimated_step_error = 5.029218706240937e-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 = 3.37505154183379e-144 estimated_step_error = 3.37505154183379e-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 = 2.264958749139141e-136 estimated_step_error = 2.264958749139141e-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 = 1.519988086615887e-128 estimated_step_error = 1.519988086615887e-128 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y2[1] (analytic) = 0 y2[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.0001 y1[1] (analytic) = 1 y1[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 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 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 x[1] = 0.1000000000000018 y2[1] (analytic) = 0.09983341664682999 y2[1] (numeric) = 0.1000000833134921 absolute error = 0.0001666666666620686 relative error = 0.1669447688559708 % Correct digits = 3 h = 0.0001 y1[1] (analytic) = 0.9950041652780256 y1[1] (numeric) = 0.9949999986113599 absolute error = 4.166666665694763e-06 relative error = 0.0004187587159025115 % Correct digits = 6 h = 0.0001 NO INFO (given) for Equation 1 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 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 x[1] = 0.2000999999999943 y2[1] (analytic) = 0.1987673364593297 y2[1] (numeric) = 0.2001026707914186 absolute error = 0.001335334332088878 relative error = 0.671807730523221 % Correct digits = 3 h = 0.0001 y1[1] (analytic) = 0.9800467060078635 y1[1] (numeric) = 0.9799799059078591 absolute error = 6.680010000437164e-05 relative error = 0.006816011889522709 % Correct digits = 5 h = 0.0001 NO INFO (given) for Equation 1 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 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 x[1] = 0.3000999999999833 y2[1] (analytic) = 0.2956157388324759 y2[1] (numeric) = 0.300120240278255 absolute error = 0.00450450144577913 relative error = 1.523769155042117 % Correct digits = 3 h = 0.0001 y1[1] (analytic) = 0.9553069323283117 y1[1] (numeric) = 0.9549689821048902 absolute error = 0.0003379502234214238 relative error = 0.0353760882481778 % Correct digits = 4 h = 0.0001 NO INFO (given) for Equation 1 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 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 x[1] = 0.4000999999999723 y2[1] (analytic) = 0.38951044646078 y2[1] (numeric) = 0.4001851144036144 absolute error = 0.01067466794283439 relative error = 2.740534442613269 % Correct digits = 3 h = 0.0001 y1[1] (analytic) = 0.921022047563425 y1[1] (numeric) = 0.919954313858983 absolute error = 0.00106773370444202 relative error = 0.1159292231132493 % Correct digits = 3 h = 0.0001 NO INFO (given) for Equation 1 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 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 ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations = 5001 Total Elapsed Time = 5.0 Seconds Elapsed Time(since restart) = 5.0 Seconds Time to Timeout = 2 Minutes 55.0 Seconds Percent Done = 100 %