随机时滞积分微分方程的稳定性分析。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-11 DOI:10.1186/s13660-018-1702-2

Yu Zhang, Longsuo Li

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引用次数: 0

摘要

本文研究了随机时滞积分微分方程数值方法的稳定性问题。对于线性随机时滞积分-微分方程，证明了在不受步长限制的情况下，分步向后欧拉法可以得到均方稳定性，而Euler- maruyama法可以在步长约束下再现均方稳定性。我们还证实了非线性随机时滞积分-微分方程的分步倒推欧拉方法的均方稳定性。数值实验进一步验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Analysis of stability for stochastic delay integro-differential equations.

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Analysis of stability for stochastic delay integro-differential equations.

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.