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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 294154, 17 pages
http://dx.doi.org/10.1155/2012/294154
Research Article

Finite Difference Method for the Reverse Parabolic Problem

1Department of Computer Technology of the Turkmen Agricultural University, Gerogly Street, 74400 Ashgabat, Turkmenistan
2Department of Mathematical Engineering, Gumushane University, 29100 Gumushane, Turkey
3Gaziosmanpaşa Lisesi, 34245 Istanbul, Turkey
4Department of Mathematics, Fatih University, 34500 Istanbul, Turkey

Received 17 April 2012; Accepted 12 June 2012

Academic Editor: Valery Covachev

Copyright © 2012 Charyyar Ashyralyyev et al. 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

A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.