Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems
作者机构：Institute of MathematicsJilin UniversityChangchun 130012P.R.China State Key Laboratory of Scientific and Engineering ComputingInstitute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences100080 BeijingP.R.China University of Chinese Academy of SciencesP.R.China
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2017年第21卷第1期
页 面：237-270页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：This work was supported by NSFC(91130003) The first authors is also supported by NSFC(11101184,11271151) the Science Foundation for Young Scientists of Jilin Province(20130522101JH) The second and third authors are also supported by NSFC(11021101,11290142).The authors would like to thank anonymous reviewers for careful reading and invaluable suggestions,which greatly improved the presentation of the paper
主 题：Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition
摘 要：We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems(SHS).Three types of systems,SHS with multiplicative noise,special separable Hamiltonians and multiple additive noise,respectively,are considered in this *** Runge-Kutta(SRK)methods for these systems are investigated,and the corresponding conditions for SRK methods to preserve the symplectic property are *** on the weak/strong order and symplectic conditions,some effective schemes are *** particular,using the algebraic computation,we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise,and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise,*** numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.
维普期刊数据库