非线性时滞-积分-微分-代数方程的龙格-库塔方法稳定性分析

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-08-10 DOI:10.1016/j.amc.2025.129675

Gehao Wang, Yuexin Yu

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引用次数: 0

摘要

本文研究了求解非线性时滞-积分-微分-代数方程的龙格-库塔方法的稳定性。利用Halanay不等式，得到了非线性DIDAEs精确解的稳定性。分析了非线性DIDAEs的龙格-库塔法和复合正交规则相结合的混合数值格式。建立了保证所提方案的全局稳定性和渐近稳定性的准则。给出了几个数值算例来验证理论结果。

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Stability analysis of Runge–Kutta methods for nonlinear delay-integro-differential-algebraic equations

This paper is devoted to examining the stability of Runge–Kutta methods for solving nonlinear delay-integro-differential-algebraic equations (DIDAEs). The stability of exact solution for nonlinear DIDAEs is obtained by using the Halanay’s inequality. Hybrid numerical schemes combining Runge–Kutta methods and compound quadrature rules are analyzed for nonlinear DIDAEs. Criteria for ensuring the global and asymptotic stability of the proposed schemes are established. Several numerical examples are provided to validate the theoretical findings.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.