The Boundary Integro-Differential Equations of a Biharmonic Boundary Value Problem

Abstract

In this paper, a new method of boundary reduction is proposed, which reduces the biharmonic boundary value problem to a system of integro-differential equations on the boundary and preserves the self-adjointness of the original problem. Moreover, a boundary finite element method based on this integro-differential equations is presented and the error estimates of the numerical approximations are given. The numerical examples show that this new method is effective.