A Survey of Some Global Methods for Solving Two-Point BVPs

Abstract

The task of comparing numerical methods which are designed to solve a particular class of problems is a notoriously difficult and inexact one. However it is important to be able to measure the quality of codes in at least a limited sense so that potential users of the software can have some guidance as to which code they might use to solve their particular problem. There are two important aspects that must be considered when numerical comparisons are contemplated. The first is to classify those codes which can be regarded as being reasonably efficient and so can set a standard against which other codes can be compared. The second is to identify some test problems which will challenge the codes and highlight any weaknesses they may have. In the present paper we consider the first of these two problems and we describe some codes which may be regarded as being amongst the most efficient for solving two-point boundary value problems at the present time. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)