%0 Journal Article
%T Approximation of Invariant Measure for Damped Stochastic Schr£żdinger Equation via Ergodic Full Discretization
%A Chuchu Chen
%A Jialin Hong
%A Xu Wang
%J Mathematics
%D 2015
%I arXiv
%X We study the approximation of invariant measure for an ergodic damped stochastic nonlinear Schr\"{o}dinger equation (NLSE) with additive noise. A spatial semi-discrete scheme and a fully discrete scheme for the damped stochastic NLSE are proposed. The ergodicity of the numerical solutions of both spatial semi-discretization and full discretization are proved. Also, we show that the approximation errors of invariant measure are $N^{-1}$ in spatial direction and $\tau^{\frac12}$ in temporal direction.
%U http://arxiv.org/abs/1509.09148v1