Frontiers of Mathematics in China >

2009 , Vol. 4 >Issue 1: 169 - 179

DOI: 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 ZHANG 1 ,
  • Yeguo SUN 1
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  • 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

Received date: 20 Mar 2008

Accepted date: 15 Nov 2008

Published date: 05 Mar 2009

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Partial functional differential equation; asymptotic stability; Euler method

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]. Frontiers of Mathematics in China, 2009 , 4(1) : 169 -179 . DOI: 10.1007/s11464-009-0007-7

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