A NOVEL WAY CONSTRUCTING SYMPLECTIC STOCHASTIC PARTITIONED RUNGE-KUTTA METHODS FOR STOCHASTIC HAMILTONIAN SYSTEMS

Xiuyan Li; Qiang Ma; Xiaohua Ding

doi:10.11948/20200315

2021 Volume 11 Issue 4

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Xiuyan Li, Qiang Ma, Xiaohua Ding. A NOVEL WAY CONSTRUCTING SYMPLECTIC STOCHASTIC PARTITIONED RUNGE-KUTTA METHODS FOR STOCHASTIC HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2070-2089. doi: 10.11948/20200315

Citation:

Xiuyan Li, Qiang Ma, Xiaohua Ding. A NOVEL WAY CONSTRUCTING SYMPLECTIC STOCHASTIC PARTITIONED RUNGE-KUTTA METHODS FOR STOCHASTIC HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2070-2089. doi: 10.11948/20200315

A NOVEL WAY CONSTRUCTING SYMPLECTIC STOCHASTIC PARTITIONED RUNGE-KUTTA METHODS FOR STOCHASTIC HAMILTONIAN SYSTEMS

1.
School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China
2.
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China

Corresponding author: Email address: lixiuyan@sdu.edu.cn(X. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (No.11901355)

Abstract

Abstract

In this paper, a novel way of constructing symplectic stochastic partitioned Runge-Kutta methods for stochastic Hamiltonian systems is presented. First, a new class of continuous-stage stochastic partitioned Runge-Kutta methods for partitioned stochastic differential equations are proposed. The order conditions of the continuous-stage stochastic partitioned Runge-Kutta methods are derived via the stochastic B-series theory. The symplectic conditions of the continuous-stage stochastic partitioned Runge-Kutta methods when applied to stochastic Hamiltonian systems are analyzed. Then we prove applying any quadrature formula to a symplectic continuous-stage stochastic partitioned Runge-Kutta method will result in a classical symplectic stochastic partitioned Runge-Kutta method. In this way, various symplectic stochastic partitioned Runge-Kutta methods can be easily constructed by using different quadrature formulas. A concrete symplectic continuous-stage stochastic partitioned Runge-Kutta method of order 1 is constructed and two retrieved stochastic partitioned Runge-Kutta methods are obtained. Numerical experiments are presented to verify the theoretical results and show the effectiveness of the derived methods.
- Stochastic Hamiltonian systems /
- symplectic /
- stochastic partitioned Runge-Kutta methods /
- continuous-stage /
- stochastic B-series
MSC: 60H10, 65P10, 37N30

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References

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