一类高振荡随机哈密顿系统的李代数方法

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英文篇名：A Lie algebraic approach for a class of highly oscillatory stochastic Hamiltonian systems 作者：阮家麟 ; 王丽瑾 英文作者：RUAN Jialin;WANG Lijin;School of Mathematical Sciences,University of Chinese Academy of Sciences; 关键词：随机微分方程数值解 ; 随机哈密顿系统 ; 高振荡随机微分方程 ; 算子分裂方法 ; 李代数方法 英文关键词：numerical solutions of stochastic differential equations;;stochastic Hamiltonian systems;;highly oscillatory SDEs;;operator splitting methods;;Lie algebraic approach 中文刊名：ZKYB 英文刊名：Journal of University of Chinese Academy of Sciences 机构：中国科学院大学数学科学学院; 出版日期：2019-01-15 出版单位：中国科学院大学学报 年：2019 期：v.36 基金：the National Nature Science Foundation of China(11471310,11071251) 语种：英文; 页：ZKYB201901002 页数：6 CN：01 ISSN：10-1131/N 分类号：8-13

摘要

为一类高振荡随机哈密顿系统提出一种李代数数值方法。对一个具体的高振荡随机哈密顿系统,给出两个基于李代数方法的数值格式,并证明它们近似保辛结构。通过数值实验展示这两种格式的根均方收敛阶,以及它们在数值求解该高振荡随机哈密顿系统中的有效性和优越性。
        In this work,we propose a Lie algebraic approach for numerically solving a class of highly oscillatory stochastic Hamiltonian systems( SHSs). For a concrete highly oscillatory SHS,we construct two numerical schemes based on the Lie algebraic approach, and prove their near preservation of the symplecticity. We also show by numerical tests their root mean-square convergence orders,as well as their effectiveness and merits in solving the highly oscillatory SHS.

引文

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