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An Euler-Maruyama Method and Its Fast Implementation for Multi-Term Fractional Stochastic Differential Equations
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  • JianFei Huang,
  • Zhenyang Huo,
  • Jingna Zhang,
  • Yifa Tang
JianFei Huang
Yangzhou University

Corresponding Author:[email protected]

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Zhenyang Huo
Yangzhou University
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Jingna Zhang
Chinese Academy of Sciences
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Yifa Tang
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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In this paper, we derive an Euler-Maruyama (EM) method for a class of multi-term fractional stochastic nonlinear differential equations, and prove its strong convergence. The strong convergence order of this EM method is $\min\{\alpha_{m}-0.5,~\alpha_{m}-\alpha_{m-1}\}$, where $\{\alpha_{i}\}_{i=1}^{m}$ is the order of Caputo fractional derivative satisfying that $1>\alpha_{m}>\alpha_{m-1}>\cdots>\alpha_{2}>\alpha_{1}>0$, $\alpha_{m}>0.5$, and $\alpha_{m}+\alpha_{m-1}>1$. Then, a fast implementation of this proposed EM method is also presented based on the sum-of-exponentials approximation technique. Finally, some numerical experiments are given to verify the theoretical results and computational efficiency of our EM method.
20 Apr 2022Submitted to Mathematical Methods in the Applied Sciences
22 Apr 2022Submission Checks Completed
22 Apr 2022Assigned to Editor
09 May 2022Reviewer(s) Assigned
12 Jul 2022Review(s) Completed, Editorial Evaluation Pending
12 Jul 2022Editorial Decision: Revise Minor
14 Jul 20221st Revision Received
15 Jul 2022Submission Checks Completed
15 Jul 2022Assigned to Editor
16 Jul 2022Reviewer(s) Assigned
18 Jul 2022Review(s) Completed, Editorial Evaluation Pending
18 Jul 2022Editorial Decision: Accept