Approximation of Invariant Measure for Damped Stochastic Nonlinear Schrödinger Equation via an Ergodic Numerical Scheme
Approximation of Invariant Measure for Damped Stochastic Nonlinear Schrödinger Equation via an Ergodic Numerical Scheme
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DOI：
10.1007/s11118-016-9583-9
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发表时间：
2015-09
影响因子：
1.1
通讯作者：
Chuchu Chen;Jialin Hong;Xu Wang
中科院分区：
文献类型：
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作者：
Chuchu Chen;Jialin Hong;Xu Wang
为了在数值上继承带加性噪声的阻尼随机非线性薛定谔方程的遍历性，我们提出了一种全离散格式，其空间方向基于谱Galerkin方法，时间方向基于隐式Euler格式的修正.我们不仅证明了空间半离散化和全离散化数值解的唯一遍历性，而且给出了不变测度的误差估计，在一定的假设下，该误差估计在空间方向上为2阶，在时间方向上为2阶.
In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schrödinger 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 orderin temporal direction under certain hypotheses.