Numerical Analysis on Ergodic Limit of Approximations for Stochastic NLS Equation via Multi-symplectic Scheme

DOI10.1137/16M1079099zbMath1382.37088arXiv1606.01510OpenAlexW2963208186MaRDI QIDQ2967593

Liying Zhang, Xu Wang, Jialin Hong

Publication date: 1 March 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.01510

zbMATH Keywords

multiplicative noisestochastic Schrödinger equationunique ergodicitymulti-symplectic scheme

Mathematics Subject Classification ID

Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (9)

Stochastic multi-symplectic Runge-Kutta methods for stochastic Hamiltonian PDEs ⋮ Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations ⋮ Analysis of a Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise ⋮ Symplectic‐preserving Fourier spectral scheme for space fractional<scp>Klein–Gordon–Schrödinger</scp>equations ⋮ A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations ⋮ Novel structure-preserving schemes for stochastic Klein-Gordon-Schrödinger equations with additive noise ⋮ CLT for approximating ergodic limit of SPDEs via a full discretization ⋮ Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients ⋮ Parareal Exponential $\theta$-Scheme for Longtime Simulation of Stochastic Schrödinger Equations with Weak Damping

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