一类随机泊松系统的保结构数值方法

doi:10.7523/j.ucas.2022.015

中国科学院大学学报 ›› 2024, Vol. 41 ›› Issue (3): 298-305.DOI: 10.7523/j.ucas.2022.015

一类随机泊松系统的保结构数值方法

刘倩倩, 王丽瑾

中国科学院大学数学科学学院, 北京 100049

收稿日期:2021-11-24 修回日期:2022-02-28 发布日期:2022-03-16
通讯作者: 王丽瑾,E-mail:ljwang@ucas.ac.cn

Structure-preserving numerical method for a class of stochastic Poisson systems

LIU Qianqian, WANG Lijin

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2021-11-24 Revised:2022-02-28 Published:2022-03-16
Supported by:
Supported by the National Natural Science Foundation of China (11971458, 11471310, 11071251)

摘要/Abstract

摘要： 考虑一类随机泊松系统，称为随机Lotka-Volterra系统的保结构数值模拟。为该类系统提出一种随机泊松积分子，并证明了该积分子具有一阶均方收敛阶。数值实验对理论结果进行了验证。

关键词: 随机泊松系统, Lotka-Volterra系统, Stratonovich 型随机微分方程, Poisson结构, Casimir函数

Abstract: In this paper, we consider the structure-preserving numerical simulation of a class of stochastic Poisson systems, i.e. the stochastic Lotka-Volterra systems. We propose a stochastic Poisson integrator for the systems which can preserve the Poisson structure and the Casimir functions of the systems, and prove that the numerical integrator has root mean-square convergence order 1. Numerical experiments are performed to verify the theoretical results.

Key words: stochastic Poisson systems, Lotka-Volterra systems, Stratonovich SDEs, Poisson structure, Casimir functions

中图分类号:

O241.8

刘倩倩, 王丽瑾. 一类随机泊松系统的保结构数值方法[J]. 中国科学院大学学报, 2024, 41(3): 298-305.

LIU Qianqian, WANG Lijin. Structure-preserving numerical method for a class of stochastic Poisson systems[J]. Journal of University of Chinese Academy of Sciences, 2024, 41(3): 298-305.

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一类随机泊松系统的保结构数值方法

Structure-preserving numerical method for a class of stochastic Poisson systems

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