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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 730804, 13 pages
http://dx.doi.org/10.1155/2012/730804
Research Article

The Numerical Solution of the Bitsadze-Samarskii Nonlocal Boundary Value Problems with the Dirichlet-Neumann Condition

1Department of Mathematics, Fatih University, 34500 Istanbul, Turkey
2Department of Mathematics, International Turkmen-Turkish University, 74400 Ashgabat, Turkmenistan
3Department of Mathematics, Uludag University, 16059 Bursa, Turkey

Received 19 March 2012; Accepted 1 May 2012

Academic Editor: Valery Covachev

Copyright © 2012 Allaberen Ashyralyev and Elif Ozturk. 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 the stable difference schemes for the numerical solution of the nonlocal boundary value problem with the Dirichlet-Neumann condition for the multidimensional elliptic equation. The first and second orders of accuracy difference schemes are presented. A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.