Delay-independent stability of Euler method for nonlinear one-dimensional diffusion equation with constant delay<sup>?

doi:10.1007/s11464-009-0007-7

Front Math Chin

2009, Vol. 4

Issue (1) : 169-179 https://doi.org/10.1007/s11464-009-0007-7

RESEARCH ARTICLE

Delay-independent stability of Euler method for nonlinear one-dimensional diffusion equation with constant delay^?

Hongjiong TIAN^1,2,3(

), Dongyue ZHANG¹, Yeguo SUN¹

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

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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

Corresponding Author(s): TIAN Hongjiong,Email:hjtian@shnu.edu.cn

Issue Date: 05 March 2009

Cite this article:

Hongjiong TIAN,Dongyue ZHANG,Yeguo SUN. Delay-independent stability of Euler method for nonlinear one-dimensional diffusion equation with constant delay^{?[J]. Front Math Chin,
2009, 4(1): 169-179.}

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0007-7
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I1/169

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