On a difference scheme of second order of accuracy for the Bitsadze-Samarskii type nonlocal boundary-value problem
1 Department of Mathematics, Fatih University, Istanbul, 34500, Turkey
2 Department of Econometrics, Canakkale Onsekiz Mart University, Canakkale, 17200, Turkey
Boundary Value Problems 2014, 2014:14 doi:10.1186/1687-2770-2014-14Published: 13 January 2014
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.