Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems  

作　　者：Peng Wang Jialin Hong Dongsheng Xu 

机构地区：[1]Institute of Mathematics,Jilin University,Changchun 130012,P.R.China [2]State Key Laboratory of Scientific and Engineering Computing,Institute of ComputationalMathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,100080 Beijing,P.R.China [3]University of Chinese Academy of Sciences,P.R.China

出　　处：《Communications in Computational Physics》2017年第1期237-270,共34页计算物理通讯（英文）

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.

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 paper.Stochastic Runge-Kutta(SRK)methods for these systems are investigated,and the corresponding conditions for SRK methods to preserve the symplectic property are given.Based on the weak/strong order and symplectic conditions,some effective schemes are derived.In 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,respectively.The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关 键 词：Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition 

分 类 号：O17[理学—数学]