Well-Posedness of a Fourth Order of Accuracy Difference Scheme for Bitsadze–Samarskii-Type Problem

In the present study, a fourth order of accuracy difference scheme for the approximate solution of the Bitsadze–Samarskii type nonlocal boundary value problem with the integral condition is investigated. Theorem on well-posedness of the difference scheme in the difference analogue of Hölder spaces with a weight is established. In applications, coercive stability estimates for the solutions of difference schemes of nonlocal boundary value problems for elliptic problems are obtained. © 2017 Taylor & Francis.