Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-05-18 DOI:10.1007/s11075-024-01846-4

Zheng Wang, Yuhao Cong

引用次数: 0

Abstract

In this paper, a class of Runge-Kutta methods for solving neutral delay differential equations (NDDEs) is proposed, which was first introduced by Bassenne et al. (J. Comput. Phys. 424, 109847, 2021) for ODEs. In the study, the explicit Runge-Kutta method is multiplied by an operator, which is a Time-Accurate and highly-Stable Explicit operator (TASE-RK), resulting in higher stability than explicit RK. Recently, the multi-parameter TASE-W method was extended by González-Pinto et al. (Appl. Numer. Math. 188, 129–145, 2023). We generalized TASE-RK and TASE-W to NDDEs for the first time. Then, by applying the argument principle, sufficient conditions for delay-dependent stability of TASE-RK and TASE-W combined with Lagrange interpolation for NDDEs are investigated. Finally, numerical examples are carried out to verify the theoretical results.

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一类中性微分方程 Runge-Kutta 方法的延迟稳定性

本文提出了一类用于求解中性延迟微分方程（NDDEs）的 Runge-Kutta 方法，该方法由 Bassenne 等人（J. Comput. Phys. 424, 109847, 2021）首次针对 ODEs 提出。在该研究中，显式 Runge-Kutta 方法乘以一个算子，即时间精确和高度稳定的显式算子 (TASE-RK)，从而获得了比显式 RK 更高的稳定性。最近，González-Pinto 等人扩展了多参数 TASE-W 方法（Appl. Numer. Math. 188, 129-145, 2023）。我们首次将 TASE-RK 和 TASE-W 推广到 NDDEs。然后，通过应用论证原理，研究了 TASE-RK 和 TASE-W 结合拉格朗日插值对 NDDEs 的延迟相关稳定性的充分条件。最后，通过数值实例验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.