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Volume 9, Number 5, 2019, Pages 1663-1685                                                                DOI:10.11948/20180254
Stochastic partitioned averaged vector field methods for stochastic differential equations with a conserved quantity
Xiuyan Li,Qiang Ma,Xiaohua Ding
Keywords:Stochastic differential equations, stochastic partitioned averaged vector field methods, conserved quantity, convergence analysis.
      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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