STOCHASTIC PARTITIONED AVERAGED VECTOR FIELD METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY

Xiuyan Li; Qiang Ma; Xiaohua Ding

doi:10.11948/20180254

2019 Volume 9 Issue 5

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Xiuyan Li, Qiang Ma, Xiaohua Ding. STOCHASTIC PARTITIONED AVERAGED VECTOR FIELD METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1663-1685. doi: 10.11948/20180254

Citation:

Xiuyan Li, Qiang Ma, Xiaohua Ding. STOCHASTIC PARTITIONED AVERAGED VECTOR FIELD METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1663-1685. doi: 10.11948/20180254

STOCHASTIC PARTITIONED AVERAGED VECTOR FIELD METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY

1.
School of Mathematics and Statistics, Shandong University, 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. 11501150) and the Key Project of Science and Technology of Weihai (No. 2014DXGJ14)

Abstract

Abstract

In this paper, stochastic differential equations in the Stratonovich sense with a conserved quantity are considered. A stochastic partitioned averaged vector field method is proposed and analyzed. We prove this numerical method is able to preserve the conserved quantity of the original system. Then the convergence analysis is carried out in detail and we derive the method is convergent with order 1 in the mean-square sense. Finally some numerical examples are reported to verify the effectiveness and flexibility of the proposed method.
- Stochastic differential equations /
- stochastic partitioned averaged vector field methods /
- conserved quantity /
- convergence analysis
MSC: 60H10, 65C20, 65C30

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References

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