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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 454831, 22 pages
http://dx.doi.org/10.1155/2012/454831
Research Article

FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions

1Department of Mathematics, Fatih University, 34500 Istanbul, Turkey
2Department of Mathematics, ITTU, 74400 Ashgabat, Turkmenistan

Received 8 April 2012; Accepted 6 May 2012

Academic Editor: Ravshan Ashurov

Copyright © 2012 Allaberen Ashyralyev and Fatma Songul Ozesenli Tetikoglu. 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 numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.