Computational and Applied Mathematics seminar

Abstract: We propose a boundary-preserving numerical scheme for the weak approximations of some scalar-valued stochastic partial differential equations (SPDEs) that only takes values in a bounded domain. We only impose regularity assumptions on the drift and diffusion coefficients locally on the domain. In particular, the drift and diffusion coefficients may be non-globally Lipschitz continuous and superlinearly growing outside the domain. The scheme consists of a finite difference discretisation in space and a Lie--Trotter splitting followed by exact simulation and exact integration in time. The scheme converges in the weak sense to the mild solution with rate 1/2 in space and 1/4 in time for globally Lipschitz continuous test functions. Numerical experiments confirm that the theoretical results are sharp and we compare the proposed scheme to existing schemes for SPDEs.