18 March 2012 10:40:07 AM PCE_ODE_HERMITE_TEST: C++ version Test PCE_ODE_HERMITE. PCE_ODE_HERMITE_TEST01: Call PCE_ODE_HERMITE to compute a polynomial chaos expansion for the ODE: u' = - alpha * u, u(0) = 1. Initial time TI = 0 Final time TF = 2 Number of time steps NT = 200 Initial condition UI = 1 Expansion degree NP = 4 E(ALPHA) ALPHA_MU = 0 STD(ALPHA) ALPHA_SIGMA = 1 i T(i) E(U(T(i))) U(T(i),0) 0 0 1 1 0 10 0.1 1.00501 1.00451 0.000506218 20 0.2 1.0202 1.01915 0.00105541 30 0.3 1.04603 1.04433 0.00169674 40 0.4 1.08329 1.0808 0.00248698 50 0.5 1.13315 1.12965 0.00349537 60 0.6 1.19722 1.19241 0.00480986 70 0.7 1.27762 1.27108 0.00654525 80 0.8 1.37713 1.36827 0.0088545 90 0.9 1.4993 1.48736 0.0119446 100 1 1.64872 1.63262 0.0160997 110 1.1 1.83125 1.80954 0.0217156 120 1.2 2.05443 2.02508 0.0293505 130 1.3 2.32798 2.28817 0.0398037 140 1.4 2.66446 2.61022 0.0542352 150 1.5 3.08022 3.00587 0.0743494 160 1.6 3.59664 3.49396 0.102681 170 1.7 4.24185 4.09882 0.143035 180 1.8 5.05309 4.85192 0.201174 190 1.9 6.07997 5.79409 0.285881 200 2 7.38906 6.97844 0.410611 PCE_ODE_HERMITE_TEST02: Examine convergence behavior as the PCE degree increases: u' = - alpha * u, u(0) = 1. Initial time TI = 0 Final time TF = 2 Number of time steps NT = 2000 Initial condition UI = 1 E(ALPHA) ALPHA_MU = 0 STD(ALPHA) ALPHA_SIGMA = 1 NP Error(NP) Log(Error(NP)) 0 6.38906 1.85459 1 3.63062 1.2894 2 1.4085 0.342522 3 0.421433 -0.864094 4 0.121242 -2.10997 5 0.0519274 -2.95791 PCE_ODE_HERMITE_TEST: Normal end of execution. 18 March 2012 10:40:07 AM