An Efficient Algorithm for Solving General Linear Two-Point BVP

Abstract

A new method is described to compute the solutions of linear BVP in an efficient and stable way. The stability is achieved by decoupling the multiple shooting recursion; this means that the choice of output points can be made virtually without regard to restrictions. By fixing the number of integration steps per “shooting” interval and assembling as many of them as is needed to fit the user’s requirements, high efficiency is gained. Apart from a mathematical description, we also give a stability analysis of the method. A large number of numerical examples confirm this analysis and illustrate the possibilities of the algorithm.