A mass-preserving splitting scheme for the stochastic Schrödinger equation with multiplicative noise

Abstract

We present a mass-preserving scheme for the stochastic nonlinear Schrödinger equation with multiplicative noise of Stratonovich type. It is a splitting scheme and we present an explicit formula for solving the sub-step related to the nonlinear part. The scheme is unconditionally stable in the L2 norm. For the linear stochastic Schrödinger equation, we prove that the scheme has a strong convergence rate in time equal to 1, which is not common for stochastic partial differential equations with noise depending on space and time. © The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.