##############ECHO OF PROBLEM################# ##############temp/mtest7postode.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; /* # */ /* # Trouble about Pi/4??? */ /* # */ 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=0.001; /* 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 = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.020046737863258e-120 estimated_step_error = 1.020046737863258e-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 = 6.845417780490904e-113 estimated_step_error = 6.845417780490904e-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 = 4.593882108541459e-105 estimated_step_error = 4.593882108541459e-105 best_h = 0.001 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 = 0.001 y1[1] (analytic) = 1 y1[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 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] = 0.1000000000000001 y2[1] (analytic) = 0.09983341664682822 y2[1] (numeric) = 0.1000000833134921 absolute error = 0.0001666666666639005 relative error = 0.1669447688578087 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9950041652780257 y1[1] (numeric) = 0.9949999986113595 absolute error = 4.166666666249874e-06 relative error = 0.0004187587159583012 % Correct digits = 6 h = 0.001 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] = 0.2000000000000001 y2[1] (analytic) = 0.1986693307950614 y2[1] (numeric) = 0.2000026641269838 absolute error = 0.001333333331922398 relative error = 0.6711319389794528 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9800665778412416 y1[1] (numeric) = 0.9799999111746031 absolute error = 6.666666663857068e-05 relative error = 0.006802258963407875 % Correct digits = 5 h = 0.001 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] = 0.3000000000000002 y2[1] (analytic) = 0.2955202066613398 y2[1] (numeric) = 0.3000202066070988 absolute error = 0.004499999945759003 relative error = 1.522738494466442 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.955336489125606 y1[1] (numeric) = 0.954998989127233 absolute error = 0.0003374999983729587 relative error = 0.03532786638159958 % Correct digits = 4 h = 0.001 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] = 0.4000000000000003 y2[1] (analytic) = 0.3894183423086507 y2[1] (numeric) = 0.400085008252919 absolute error = 0.01066666594426829 relative error = 2.739127767077278 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.921060994002885 y1[1] (numeric) = 0.9199943273651138 absolute error = 0.001066666637771219 relative error = 0.1158084692236872 % Correct digits = 3 h = 0.001 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 = 500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %