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

Ashyralyev A., Ozturk E.

BOUNDARY VALUE PROBLEMS, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2014
  • Doi Number: 10.1186/1687-2770-2014-14
  • Journal Name: BOUNDARY VALUE PROBLEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Çanakkale Onsekiz Mart University Affiliated: Yes

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 Holder spaces with a weight is proved. The theoretical statements for the solution of this difference scheme are supported by the results of numerical example.