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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 230190, 13 pages
http://dx.doi.org/10.1155/2012/230190
Research Article

On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

Department of Mathematics, Fatih University, 34500 Buyukcekmece, Istanbul, Turkey

Received 7 April 2012; Accepted 24 April 2012

Academic Editor: Ravshan Ashurov

Copyright © 2012 Allaberen Ashyralyev and Okan Gercek. 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 are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.