Open Access Research

On a difference scheme of second order of accuracy for the Bitsadze-Samarskii type nonlocal boundary-value problem

Allaberen Ashyralyev1 and Elif Ozturk2*

Author Affiliations

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

2 Department of Econometrics, Canakkale Onsekiz Mart University, Canakkale, 17200, Turkey

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Boundary Value Problems 2014, 2014:14  doi:10.1186/1687-2770-2014-14

Published: 13 January 2014

Abstract

In this study, the Bitsadze-Samarskii type nonlocal boundary-value problem with integral condition for an elliptic differential equation in a Hilbert space H with self-adjoint positive definite operator A is considered. The second order of the accuracy difference scheme for the approximate solutions of this nonlocal boundary-value problem is presented. The well-posedness of this difference scheme in Hölder spaces with a weight is proved. The theoretical statements for the solution of this difference scheme are supported by the results of numerical example.

Keywords:
well-posedness; difference scheme; elliptic equation