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

作　　者：刘倩倩 王丽瑾 LIU Qianqian;WANG Lijin(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2024年第3期298-305,共8页Journal of University of Chinese Academy of Sciences

基　　金：Supported by the National Natural Science Foundation of China(11971458,11471310,11071251)。

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。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.

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 

分 类 号：O241.8[理学—计算数学]