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Numerical Algorithms

18.05.2024 | Original Paper

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

verfasst von: Zheng Wang, Yuhao Cong

Erschienen in: Numerical Algorithms

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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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Titel: Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations
verfasst von: Zheng Wang
Yuhao Cong
Publikationsdatum: 18.05.2024
Verlag: Springer US
Erschienen in: Numerical Algorithms
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-024-01846-4

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