ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS  

作　　者：韩豪 张诚坚 Hao HAN;Chengjian ZHANG(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)

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [2]Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Acta Mathematica Scientia》2023年第4期1865-1880,共16页数学物理学报（B辑英文版）

基　　金：the NSFC(11971010)。

摘　　要：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.

关 键 词：neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment 

分 类 号：O241.82[理学—计算数学]