Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations
Year: 2022
Author: Mingzhan Song, Songhe Song, Wei Zhang, Xu Qian
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 4 : pp. 912–927
Abstract
In this paper, the global momentum conservation laws and the global momentum evolution laws are presented for the two-dimensional stochastic nonlinear Schrödinger equation with multiplicative noise and the two-dimensional stochastic Klein-Gordon equation with additive noise, respectively. In order to preserve the global momenta or their changing trends in numerical simulation, the schemes are constructed by using a stochastic multi-symplectic formulation. It is shown that under periodic boundary conditions, the schemes have discrete global momentum conservation laws or the discrete global momentum evolution laws. Numerical experiments confirm global momentum-preserving properties of the schemes and their mean square convergence in the time direction.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.110122.040522
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 4 : pp. 912–927
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Stochastic global momentum-preserving scheme stochastic nonlinear Schrödinger equation global momentum conservation law stochastic Klein-Gordon equation global momentum evolution law.