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

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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