The fast Euler-Maruyama method for solving multiterm Caputo fractional stochastic delay integro-differential equations

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-09-03 DOI:10.1007/s11075-024-01925-6

Huijiao Guo, Jin Huang, Yi Yang, Xueli Zhang

引用次数: 0

Abstract

This paper studies a type of multiterm fractional stochastic delay integro-differential equations (FSDIDEs). First, the Euler-Maruyama (EM) method is developed for solving the equations, and the strong convergence order of this method is obtained, which is \(\varvec{\min \left\{ \alpha _{l}-\frac{1}{2}, \alpha _{l}-\alpha _{l-1}\right\} }\). Then, a fast EM method is also presented based on the exponential-sum-approximation with trapezoid rule to cut down the computational cost of the EM method. In the end, some concrete numerical experiments are used to substantiate these theoretical results and show the effectiveness of the fast method.

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求解多期卡普托分数随机延迟积分微分方程的快速欧拉-丸山方法

本文研究了一种多期分数随机延迟积分微分方程（FSDIDEs）。首先，建立了求解该方程的 Euler-Maruyama (EM) 方法，并得到了该方法的强收敛阶数，即 \(\varvec{min \left\{ \alpha _{l}-\frac{1}{2}, \alpha _{l}-\alpha _{l-1}\right\} 。}\).然后，还提出了一种基于梯形法则的指数和逼近的快速 EM 方法，以降低 EM 方法的计算成本。最后，通过一些具体的数值实验来证实这些理论结果，并展示了快速方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.