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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 603018, 14 pages
http://dx.doi.org/10.1155/2012/603018
Research Article

The Difference Problem of Obtaining the Parameter of a Parabolic Equation

1Department of Computer Technology, Turkmen Agricultural University, Gerology Street,74400 Asgabat, Turkmenistan
2Department of Mathematical Engineering, Gumushane University, 29100 Gumushane, Turkey
3Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey

Received 4 April 2012; Accepted 23 April 2012

Academic Editor: Ravshan Ashurov

Copyright © 2012 Charyyar Ashyralyyev and Oznur Demirdag. 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 boundary value problem of determining the parameter 𝑝 of a parabolic equation 𝜐 ( 𝑡 ) + 𝐴 𝜐 ( 𝑡 ) = 𝑓 ( 𝑡 ) + 𝑝 ( 0 𝑡 1 ) , 𝜐 ( 0 ) = 𝜑 , 𝜐 ( 1 ) = 𝜓 in an arbitrary Banach space 𝐸 with the strongly positive operator 𝐴 is considered. The first order of accuracy stable difference scheme for the approximate solution of this problem is investigated. The well-posedness of this difference scheme is established. Applying the abstract result, the stability and almost coercive stability estimates for the solution of difference schemes for the approximate solution of differential equations with parameter are obtained.