A Decoupling and Coupling Approach for the Bi-harmonic Equation

Abstract

This paper is devoted to the numerical solution of the bi-harmonic problem: Δ2 w = p . The operator is split into two harmonic ones. The finite difference scheme of the harmonic operator is used to get discretized operators, coupling those leads to a global system , this system is to be solved with any well-posed boundary conditions. In this way, boundary conditions need not be specified with the decoupled equations, but rather with the global system. Numerical test problems are provided. The extension of this technique to poly harmonic equations is straightforward.