Abstract and Applied Analysis
Volume 6 (2001), Issue 5, Pages 267-297
doi:10.1155/S1085337501000616

On the stability of the linear delay differential and difference equations

A. Ashyralyev1,2 and P. E. Sobolevskii3

1Department of Mathematics, Fatih University, Buyukcekmece, Istanbul 34900, Turkey
2Department of Mathematics, International Turkmen-Turkish University, 84, Gerogly, Ashgabat 744012, Turkmenistan
3Institute of Mathematics, Hebrew University, Jerusalem, Israel

Received 14 August 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the initial-value problem for linear delay partial differential equations of the parabolic type. We give a sufficient condition for the stability of the solution of this initial-value problem. We present the stability estimates for the solutions of the first and second order accuracy difference schemes for approximately solving this initial-value problem. We obtain the stability estimates in Hölder norms for the solutions of the initial-value problem of the delay differential and difference equations of the parabolic type.