Multiple shooting with dichotomically stable formulae for linear boundary-value problems

Abstract

This paper describes an improvement of England and Mattheij's code MUTSSYM for solving linear Boundary-Value Problems for Ordinary Differential Equations, which may or not give rise to sharp Boundary Layers. The method is based on Multiple Shooting with a Decoupling strategy, allowing the calculation of stable solutions according to the increasing or decreasing fundamental modes. The integration of the associated Initial-Value Problems is performed using a 4(th)-order symmetric implicit Runge-Kutta method with the Dichotomic Stability property. If the problem is well conditioned, the method calculates discrete decaying (growing) modes controlled by initial (terminal) conditions corresponding to similar continuous modes. A special step-size control strategy permits efficient calculation of the numerical solution throughout the interval. (C) 1999 Elsevier Science Ltd. All rights reserved.