Split-step θ-method for stochastic pantograph differential equations: Convergence and mean-square stability analysis

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-06-02 DOI:10.1016/j.apnum.2025.05.010

Fathalla A. Rihan, K. Udhayakumar

引用次数: 0

Abstract

This paper introduces a split-step θ-method (SSθ-method) with variable step sizes for solving stochastic pantograph delay differential equations (SPDDEs). We establish the mean-square convergence of the proposed SSθ-method and show that it achieves a strong convergence order of order 1/2. Under certain assumptions, we prove that the SSθ-method is exponentially mean-square stable for

θ \geq 0.5

. Additionally, we analyze the asymptotic mean-square stability of the SSθ-method under a stronger assumption. Finally, numerical examples illustrate the effectiveness of the proposed methods.

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随机受电弓微分方程的裂步θ-法：收敛性和均方稳定性分析

介绍了求解随机受电弓延迟微分方程（SPDDEs）的变步长裂步θ法（ss θ法）。我们建立了所提出的s θ-方法的均方收敛性，并证明了它具有1/2阶的强收敛阶。在一定的假设条件下，证明了当θ≥0.5时，s θ-方法是指数均方稳定的。此外，在更强的假设下，我们分析了s θ-方法的渐近均方稳定性。最后，通过数值算例验证了所提方法的有效性。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.