On a Nonlocal Contact Problem for Elliptic Equation in Rectangular Area

Abstract:  Nonlocal contact problem for two-dimensional linear elliptic equations is stated and investigated.  The method of separation of variables is used to find the solution of a stated problem in the case of Poisson's equation.  Then, the more general problem with nonlocal multipoint contact conditions for elliptic equation with variable coefficients is considered, and the iterative method to solve the problem numerically is constructed and investigated.  The uniqueness and existence of the regular solution are proved.  The iterative method allows reducing the solution of a nonlocal contact problem to the solution of a sequence of classical boundary value problems. The numerical experiment is conducted. The results fully agree with the theoretical conclusions and show the efficiency of the proposed iterative procedure.