Continuous orthonormalization for boundary value problems

Abstract

Continuous orthonormalization describes an initial value method for linear 2-point boundary value problems which provides an orthogonal basis for the solution space at all points of the interval. In this paper the equations of continuous orthonormalization are derived with elementary projection arguments to provide geometric insight and motivate some modifications of an earlier algorithm. The method is then applied to some oscillatory and stiff boundary value problems to demonstrate that it is simple to use, problem independent, and as adaptive as the initial value code which is used to integrate the equations of continuous orthonormalization.