title: On the long time simulation of reaction-diffusion equations with delay.
abstract: For a consistent numerical method to be practically useful, it is widely accepted that it must preserve the asymptotic stability of the original continuous problem. However, in this study, we show that it may lead to unreliable numerical solutions in long time simulation even if a classical numerical method gives a larger stability region than that of the original continuous problem. Some numerical experiments on the reaction-diffusion equations with delay are presented to confirm our findings. Finally, some open problems on the subject are proposed.
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
authors.forename: Dongfang
authors.identifier: 0000-0002-6234-2714
authors.initials: D
authors.lastname: Li
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
authors.forename: Chengjian
authors.initials: C
authors.lastname: Zhang
mesh_terms: D008962:Models, Theoretical