Convergence of a \(\theta \)-scheme to solve the stochastic nonlinear Schrödinger equation with Stratonovich noise

DOI10.1007/s40072-015-0062-xzbMath1362.65012arXiv1410.6231OpenAlexW2227679799WikidataQ115375280 ScholiaQ115375280MaRDI QIDQ2629198

Jialin Hong, Chuchu Chen, Andreas Prohl

Publication date: 5 July 2016

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6231

zbMATH Keywords

stabilityconvergencenumerical exampleHamiltonianstochastic Schrödinger equationStratonovich noise\(\theta\) scheme

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (10)

Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise ⋮ A charge-preserving compact splitting method for solving the coupled stochastic nonlinear Schrödinger equations ⋮ Analysis of a Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise ⋮ Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion ⋮ Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations ⋮ Fluctuations and temperature effects in bose-einstein condensation ⋮ Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations ⋮ Strong Convergence of Full Discretization for Stochastic Cahn--Hilliard Equation Driven by Additive Noise ⋮ Strong convergence rate of finite difference approximations for stochastic cubic Schrödinger equations ⋮ Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise

Cites Work

• Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation
• A semi-discrete scheme for the stochastic nonlinear Schrödinger equation
• A concise course on stochastic partial differential equations
• Equations stochastiques du type Navier-Stokes
• Order of Convergence of Splitting Schemes for Both Deterministic and Stochastic Nonlinear Schrödinger Equations
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Rates of Convergence for Discretizations of the Stochastic Incompressible Navier--Stokes Equations
• Numerical simulation of focusing stochastic nonlinear Schrödinger equations

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