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Delay-independent stability of Euler method for nonlinear one-dimensional diffusion equation with constant delay |
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| Authors: | Hongjiong Tian Dongyue Zhang Yeguo Sun |
| Affiliation: | (1) Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China;(2) Division of Computational Science, E-Institute of Shanghai Universities, Shanghai, 200234, China;(3) Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China |
| Abstract: | This paper is concerned with delay-independent asymptotic stability of a numerical process that arises after discretization of a nonlinear one-dimensional diffusion equation with a constant delay by the Euler method. Explicit sufficient and necessary conditions for the Euler method to be asymptotically stable for all delays are derived. An additional restriction on spatial stepsize is required to preserve the asymptotic stability due to the presence of the delay. A numerical experiment is implemented to confirm the results. |
| Keywords: | Partial functional differential equation asymptotic stability Euler method |
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