1 - Introduction

While research in Numerical methods for solving boundary-value problems (BVPs) for ordinary differential equations (ODEs) has been very active for some time, robust software for solving these problems has only recently been developed and partially tested. A few codes based on shooting, multiple shooting, other initial-value techniques, and finite differences with deferred corrections have been reported.

Despite these advances, the accessibility of BVP software is at this time considerably behind that for initial-value problems (IVP), as evidenced by the fact that the large numerical librairies, for example, NAG and IMSL, contain either a simple shooting code or nothing at all for BVPs while having several advanced packages for IVPs> This is partially due to the fact that most of the above mentioned codes are undergoing fairly regular modification.

COLSYS is a code for solving mixed order systems of boundary value problems in ordinary differential equations. The method of spline collocation at Gaussian points is implemented using a B-spline basis. Approximate solutions are computed on a sequence of automatically selected meshes until a user-specified set of tolerances is satisfied. A damped Newton's method is used for the nonlinear iteration. The code has been found to be particularly effective for difficult problem. The Authors are:

U. ASCHER

University of British Columbia, Canada

J. CHRISTIANSEN and R. D. RUSSELL

Simon Fraser University, Canada