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Asymptotical Stability of Neutral Reaction-Diffusion Equations with PCAS and Their Finite Element Methods
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Asymptotical Stability of Neutral Reaction-Diffusion Equations with PCAS and Their Finite Element Methods
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Journal Article
Asymptotical Stability of Neutral Reaction-Diffusion Equations with PCAS and Their Finite Element Methods
2023
Overview
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments. First, for the analytical solutions of the equations, we derive their expressions and asymptotical stability criteria. Second, for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations, we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable. Finally, with a typical example with numerical experiments, we illustrate the applicability of the obtained theoretical results.
Publisher
Springer Nature Singapore,Springer Nature B.V,School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China,Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China
