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

This paper describes an improvement of England and Mattheij's code MUTSSYM for solving linear Boundary-Value Problems for Ordinary Differential Equati ons, which may or not give rise to sharp Boundary Layers. The method is based on Multiple Shooting with a Decoupling strategy, allowi ng the calculation of stable solutions according to the increasing or decre asing 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 St ability property. If the problem is well conditioned, the method calculates discrete decaying (growing) modes controlled by initial (terminal) conditi ons 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.