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Volume 12, Issue 4
Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations

Mingzhan Song, Songhe Song, Wei Zhang & Xu Qian

DOI: 10.4208/eajam.110122.040522

East Asian J. Appl. Math., 12 (2022), pp. 912-927.

Published online: 2022-08

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  • 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.

  • Keywords

Stochastic global momentum-preserving scheme, stochastic nonlinear Schrödinger equation, global momentum conservation law, stochastic Klein-Gordon equation, global momentum evolution law.

  • AMS Subject Headings

65M06, 65P10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{EAJAM-12-912, author = {Song , MingzhanSong , SongheZhang , Wei and Qian , Xu}, title = {Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.110122.040522}, url = {http://global-sci.org/intro/article_detail/eajam/20890.html} }
TY - JOUR T1 - Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations AU - Song , Mingzhan AU - Song , Songhe AU - Zhang , Wei AU - Qian , Xu JO - East Asian Journal on Applied Mathematics VL - 4 SP - 912 EP - 927 PY - 2022 DA - 2022/08 SN - 12 DO - http://doi.org/10.4208/eajam.110122.040522 UR - https://global-sci.org/intro/article_detail/eajam/20890.html KW - Stochastic global momentum-preserving scheme, stochastic nonlinear Schrödinger equation, global momentum conservation law, stochastic Klein-Gordon equation, global momentum evolution law. AB -

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.

Song , MingzhanSong , SongheZhang , Wei and Qian , Xu. (2022). Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations. East Asian Journal on Applied Mathematics. 12 (4). 912-927. doi:10.4208/eajam.110122.040522
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