Iterative continuation and the solution of nonlinear two-point boundary value problems

In this paper we present a unified function theoretic approach for the numerical solution of a wide class of two-point boundary value problems. The approach generates a class of continuous analog iterative methods which are designed to overcome some of the essential difficulties encountered in the numerical treatment of two-point problems. It is shown that the methods produce convergent sequences of iterates in cases where the initial iterate (guess),x ₀, is far from the desired solution. The results of some numerical experiments using the methods on various boundary value problems are presented in a forthcoming paper.