The effect of a new two-point nonlocal condition on the eigenvalue problem of the difference scheme for an elliptic partial differential equation

Abstract

In this paper, a new form of two-point nonlocal boundary conditions is presented. This condition generalizes a Dirichlet condition at one boundary and a mixed condition at the other one. The focus of this work is not the numerical solution of the considered problem. Rather, we study the effect of the proposed nonlocal boundary condition on the difference eigenvalue problem for an elliptic partial differential equation in one and two dimensions.

Keywords

• Elliptic partial differential equation
• Non-local boundary condition
• Eigenvalues and eigenvectors problem
• Finite difference method