Report

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in time and second order in the spatial grid size, and that the discretisation is stable with respect to boundary data. Numerical experiments clearly indicate that the same convergence order also holds for boundary-value problem...