Analysis of the factorization method for elliptic differential equations

Abstract

This paper presents a numerical analysis of the method of factorization for elliptic boundary value problems. A second-order elliptic boundary value problem is transformed into a decoupled system of first-order initial value problems. This elaborates the decoupled system's occupying operator, the solution of the problem, and the affine part of the operator. The solution of the problem is thus obtained by solving the factorized system using the finite-element method. A comparative study is made with the help of an example that illustrates many of its properties.