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arXiv · 1509.09148

Approximation of Invariant Measure for Damped Stochastic Nonlinear Schr\"{o}dinger Equation via an Ergodic Numerical Scheme

Chuchu Chen·Jialin Hong·Xu Wang
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Abstract

In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal direction is based on a modification of the implicit Euler scheme. We not only prove the unique ergodicity of the numerical solutions of both spatial semi-discretization and full discretization, but also present error estimations on invariant measures, which gives order $2$ in spatial direction and order ${\frac12}$ in temporal direction.

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Chuchu Chen, Jialin Hong, Xu Wang. 2015-09-30. Approximation of Invariant Measure for Damped Stochastic Nonlinear Schr\"{o}dinger Equation via an Ergodic Numerical Scheme. https://arxiv.org/abs/1509.09148

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