Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations

DOI10.1016/j.jde.2018.10.034zbMath1431.60066arXiv1701.05680OpenAlexW2581568259MaRDI QIDQ1736178

Jianbo Cui, Jialin Hong, Zhihui Liu, Weien Zhou

Publication date: 26 March 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.05680

zbMATH Keywords

splitting schemeexponential integrabilitystochastic nonlinear Schrödinger equationstrong convergence ratenon-monotone coefficients

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Foundations of stochastic processes (60G05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Splitting up method for the 2D stochastic Navier-Stokes equations
• Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation
• Taylor expansions of solutions of stochastic partial differential equations with additive noise
• On the splitting-up method and stochastic partial differential equations
• Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion
• Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
• Strong convergence rate of finite difference approximations for stochastic cubic Schrödinger equations
• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
• Exponential moments for numerical approximations of stochastic partial differential equations
• A Milstein scheme for SPDEs
• Convergence of a \(\theta \)-scheme to solve the stochastic nonlinear Schrödinger equation with Stratonovich noise
• Order of Convergence of Splitting Schemes for Both Deterministic and Stochastic Nonlinear Schrödinger Equations
• A mass-preserving splitting scheme for the stochastic Schrodinger equation with multiplicative noise
• Semigroup Splitting and Cubature Approximations for the Stochastic Navier–Stokes Equations
• Finite element approximations for second-order stochastic differential equation driven by fractional Brownian motion
• Analysis of a Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise
• Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
• On the discretisation in time of the stochastic Allen–Cahn equation
• Exponential Integrators for Stochastic Schrödinger Equations Driven by Itô Noise
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Approximating Stochastic Evolution Equations with Additive White and Rough Noises
• Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations

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