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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 178084, 18 pages
http://dx.doi.org/10.1155/2012/178084
Research Article

A Note on the Stability of the Integral-Differential Equation of the Parabolic Type in a Banach Space

Department of Mathematics and Computer Sciences, Bahcesehir University, Besiktas, 34353 Istanbul, Turkey

Received 20 May 2012; Accepted 15 June 2012

Academic Editor: Ravshan Ashurov

Copyright © 2012 Maksat Ashyraliyev. 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

The integral-differential equation of the parabolic type in a Banach space is considered. The unique solvability of this equation is established. The stability estimates for the solution of this equation are obtained. The difference scheme approximately solving this equation is presented. The stability estimates for the solution of this difference scheme are obtained.