A note on the well-posedness of the nonlocal boundary value problem for elliptic difference equations

Abstract

The nonlocal boundary value problem for elliptic difference equations in an arbitrary Banach space is considered. The well-posedness of this problem is investigated. The stability, almost coercive stability and coercive stability estimates for the solutions of difference schemes of the second order of accuracy for the approximate solutions of the nonlocal boundary value problem for elliptic equation are obtained. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments. © 2005 Elsevier Inc. All rights reserved. © 2008 Elsevier B.V., All rights reserved.