@Article{IJNAM-21-104,
author = {Liu , Qianqian and Wang , Lijin},
title = {Lie-Poisson Numerical Method for a Class of Stochastic Lie-Poisson Systems },
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {1},
pages = {104--119},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1004},
url = {http://global-sci.org/intro/article_detail/ijnam/22330.html}
}