Year: 2024
Author: Qianqian Liu, Lijin Wang
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 104–119
Abstract
We propose a numerical method based on the Lie-Poisson reduction for a class of stochastic Lie-Poisson systems. Such system is transformed to SDE on the dual $\mathfrak{g}^∗$ of the Lie algebra related to the Lie group manifold where the system is located, which is also the reduced form of a stochastic Hamiltonian system on the cotangent bundle of the Lie group by momentum mapping. Stochastic Poisson integrators are obtained by discretely reducing stochastic symplectic methods on the cotangent bundle to integrators on $\mathfrak{g}^∗.$ Stochastic generating functions creating stochastic symplectic methods are used to construct the schemes. An application to the stochastic rigid body system illustrates the theory and provides numerical validation of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1004
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 104–119
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Stochastic Lie-Poisson systems structure-preserving algorithms Poisson integrators Lie-Poisson reduction Poisson structure Casimir functions.