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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The authors are grateful to the editor and anonymous reviewers for the valuable suggestions which improve this paper greatly.
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This work was supported by the National Natural Science Foundation of China (Grant No.12271340 and No.12371399), Natural Science Foundation of Shanghai (21ZR1426400).
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Zheng Wang: Conceptualization, Methodology, Software, Writing-original draft. Yuhao Cong: Conceptualization, Writing-review, Fund. All authors reviewed the manuscript.
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Wang, Z., Cong, Y. Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01846-4
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DOI: https://doi.org/10.1007/s11075-024-01846-4