Numerical Solution And Error Evaluation Of A Nonlocal Boundary Problem For Elliptic Equation In Partial Derivatives

Abstract

In a rectangular domain, a nonlocal boundary value problem for an elliptic equation is considered. The corresponding difference problem was constructed and the error of the approximate solution was estimated.

           Many applied problems of heat conduction [1], [2], [3], fluid mechanics [4], and the theory of elasticity and shells [5] lead to nonlocal boundary value problems for partial differential equations. Non-local boundary conditions are especially difficult for justification of classical finite difference schemes due to the complexity of the structure of the matrices obtained from systems of equations. This difficulty manifests itself especially in the justification of numerical methods in the case of non-linear equations. In this paper, we study a nonlocal boundary value problem for a quasilinear equation. The method of finite differences was applied to the numerical solution of the problem posed, and the error of the approximate solution of the nonlocal problem was estimated.