Time integration of dissipative stochastic PDEs

Abstract

The paper is focused on the numerical solution of stochastic reaction-diffusion problems. A special attention is addressed to the conservation of mean-square dissipativity in the time integration of the spatially discretized problem, obtained by means of finite differences. The analysis highlights the conservative ability of stochastic $\theta$-methods and stochastic $\theta$-IMEX methods, emphasizing the roles of spatial and temporal stepsizes. A selection of numerical experiments is provided, confirming the theoretical expectations.