Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems. (5th December 2016)

• Record Type: Journal Article
• Authors: Wang, Peng; Hong, Jialin; Xu, Dongsheng
• Is Part Of: Communications in computational physics. Volume 21:Number 1(2017:Jan.)
• Page Start: 237
• Page End: 270
• Publication Date: 2016-12-05
• Subjects: 65C30, -- 60H35, -- 65P10; Stochastic differential equation, -- Stochastic Hamiltonian system, -- symplectic integration, -- Runge-Kutta method, -- order condition; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.261014.230616a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: 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.