Stochastic symplectic partitioned Runge-Kutta methods for stochastic Hamiltonian systems with multiplicative noise

被引：18

作者：

Ma, Qiang ^{[1
]}

Ding, Xiaohua ^{[1
]}

机构：

[1] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 252卷

基金：

中国国家自然科学基金;

关键词：

Stochastic Hamiltonian systems; Stochastic differential equations; Symplectic integrators; Stochastic generating functions; Stochastic partitioned Runge-Kutta methods; DIFFERENTIAL-DELAY EQUATIONS; MILSTEIN METHODS; STABILITY; CONVERGENCE;

D O I：

10.1016/j.amc.2014.12.045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some new stochastic partitioned Runge-Kutta (SPRK) methods are proposed for the strong approximation of partitioned stochastic differential equations (SDEs). The order conditions up to strong global order 1.0 are calculated. The SPRK methods are applied to solve stochastic Hamiltonian systems with multiplicative noise. Some conditions are captured to guarantee that a given SPRK method is symplectic. It is shown that stochastic symplectic partitioned Runge-Kutta (SSPRK) methods can be written in terms of stochastic generating functions. In addition, this paper also proves that the SSPRK methods can conserve the quadratic invariants of original stochastic systems. Based on the order and symplectic conditions, some low-stage SSPRK methods with strong global order 1.0 are constructed. Finally, some numerical results are presented to demonstrate the efficiency of the SSPRK methods. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：520 / 534

页数：15

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