Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

被引：19

作者：

Wang, Peng ^{[1
]}

Hong, Jialin ^{[2
]}

Xu, Dongsheng ^{[2
,3
]}

机构：

[1] Jilin Univ, Inst Math, Changchun 130012, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China

[3] Univ Chinese Acad Sci, Beijing, Peoples R China

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2017年 / 21卷 / 01期

关键词：

Stochastic differential equation; Stochastic Hamiltonian system; symplectic integration; Runge-Kutta method; order condition; DIFFERENTIAL-EQUATIONS; APPROXIMATION; INTEGRATORS;

D O I：

10.4208/cicp.261014.230616a

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页码：237 / 270

页数：34