On One Generalization of the Multipoint Nonlocal Contact Problem for Elliptic Equation in Rectangular Area

TL;DR

This paper extends the nonlocal contact problem for elliptic equations in a rectangular area, introducing a more general multipoint contact condition, and develops an iterative numerical method with proven convergence.

Contribution

It generalizes the nonlocal contact problem for elliptic equations with variable coefficients and constructs an iterative method for its numerical solution.

Findings

Proved uniqueness and existence of the regular solution.

Developed an iterative method reducing the problem to classical boundary value problems.

Validated the method's effectiveness for the generalized problem.

Abstract

A 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 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 is proved. The iterative method allows to reduce the solution of a nonlocal contact problem to the solution of a sequence of classical boundary value problems.