This article is cited in 17 papers

On the solution of a nonlocal problem

E. A. Volkov^a, A. A. Dosiyev^b, S. C. Buranay<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russia
^b Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Cyprus, Mersin 10, Turkey

Abstract: In a rectangular domain, we consider the Bitsadze–Samarskii nonlocal boundary value problem for the two-dimensional Poisson equation. The solution of this problem is defined as a solution of the local Dirichlet boundary value problem, by constructing a special method to find a function as the boundary value on the side of the rectangle, where the nonlocal condition was given. Further, the five point approximation of the Laplace operator is used for the realization of the proposed method. Numerical experiments are illustrated in the last section to support the analysis made.

Received: 06.02.2013
Revised: 06.05.2013
Accepted: 19.05.2013

Language: English

DOI: 10.1016/j.camwa.2013.05.010

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