Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise

We compare Wiener chaos and stochastic collocation methods for linear advectionreaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multistage algorithm for long-time integration. We derive error estimates for both methods and compare their numerical performance. Numerical results confirm that the recursive multistage stochastic collocation method is of order Δ (time step size) in the second-order moments while the recursive multistage Wiener chaos method is of order ΔN + Δ2 (N is the order of Wiener chaos) for advection-diffusion-reaction equations with commutative noises, in agreement with the theoretical error estimates. However, for noncommutative noises, both methods are of order one in the second-order moments.