Abstract
We consider a nonlocal boundary-value problem for the Poisson equation in a rectangular domain. Dirichlet conditions are posed on a pair of adjacent sides of a rectangle, and integral constraints are given instead of standard boundary conditions on the other pair. The corresponding difference scheme is constructed and investigated; an a priori estimate of the solution is obtained with the help of energy inequality method. Discretization error estimate that is compatible with the smoothness of the solution sought is obtained.
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Berikelashvili, G., Khomeriki, N. On the convergence of difference schemes for one nonlocal boundary-value problem. Lith Math J 52, 353–362 (2012). https://doi.org/10.1007/s10986-012-9178-0
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DOI: https://doi.org/10.1007/s10986-012-9178-0