Please use this identifier to cite or link to this item: https://doi.org/10.1137/12088416X
Title: Order of convergence of splitting schemes for both deterministic and stochastic nonlinear Schrödinger equations
Authors: Liu, J. 
Keywords: Mass preserving
Nonlinear Schrödinger equation
Splitting scheme
Stochastic partial differential equation
Strang splitting
Issue Date: 2013
Citation: Liu, J. (2013). Order of convergence of splitting schemes for both deterministic and stochastic nonlinear Schrödinger equations. SIAM Journal on Numerical Analysis 51 (4) : 1911-1932. ScholarBank@NUS Repository. https://doi.org/10.1137/12088416X
Abstract: We first prove the second order convergence of the Strang-type splitting scheme for the nonlinear Schrödinger equation. The proof does not require commutator estimates but crucially relies on an integral representation of the scheme. It reveals the connection between Strang-type splitting and the midpoint rule. We then show that the integral representation idea can also be used to study the stochastic nonlinear Schrödinger equation with multiplicative noise of Stratonovich type. Even though the nonlinear term there is not globally Lipschitz, we prove the first order convergence of a splitting scheme of it. Both schemes preserve the mass. They are very efficient because they use explicit formulas to solve the subproblems containing the nonlinear or the nonlinear plus stochastic terms. © 2013 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Numerical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/103883
ISSN: 00361429
DOI: 10.1137/12088416X
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