Stochastic partitioned averaged vector field methods for stochastic differential equations with a conserved quantity

Xiuyan Li; Qiang Ma; Xiaohua Ding

doi:10.11948/20180254

Stochastic partitioned averaged vector field methods for stochastic differential equations with a conserved quantity

Xiuyan Li^*
, Qiang Ma
, Xiaohua Ding

^*Corresponding author for this work

Shandong University
Harbin Institute of Technology Weihai

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	1663-1685
Number of pages	23
Journal	Journal of Applied Analysis and Computation
Volume	9
Issue number	5
DOIs	https://doi.org/10.11948/20180254
State	Published - Oct 2019
Externally published	Yes

Keywords

Conserved quantity
Convergence analysis
Stochastic differential equations
Stochastic partitioned averaged vector field methods

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10.11948/20180254

Cite this

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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.",

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author = "Xiuyan Li and Qiang Ma and Xiaohua Ding",

year = "2019",

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AU - Ding, Xiaohua

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N2 - 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.

AB - 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.

KW - Conserved quantity

KW - Convergence analysis

KW - Stochastic differential equations

KW - Stochastic partitioned averaged vector field methods

UR - https://www.scopus.com/pages/publications/85073575157

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DO - 10.11948/20180254

M3 - 文章

AN - SCOPUS:85073575157

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JO - Journal of Applied Analysis and Computation

JF - Journal of Applied Analysis and Computation

IS - 5

ER -

Stochastic partitioned averaged vector field methods for stochastic differential equations with a conserved quantity

Abstract

Keywords

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