Full Discretization of Stochastic Semilinear Schrödinger equation driven by multiplicative Wiener noise

Abstract

In this article, we have analyzed the full discretization of the Stochastic semilinear Schrödinger equation in a bounded convex polygonal domain driven by multiplicative Wiener noise. We use the finite element method for spatial discretization and the stochastic trigonometric method for time discretization and derive a strong convergence rate with respect to both parameters (temporal and spatial). Numerical experiments have also been performed to support theoretical bounds.

27 pages, Comments are welcome