Title: On the development of effective algorithms for the numerical solution of singularly perturbed two-point boundary value problems

Authors: Steven Capper, Jeff Cash, Francesca Mazzia

Addresses: Department of Mathematics, Imperial College, South Kensington, London, UK. ' Department of Mathematics, Imperial College, South Kensington, London, UK. ' Dipartimento di Matematica, Universita di Bari, Via Orabona 4, I-70125 Bari, Italy

Abstract: Singular perturbation boundary value problems have proved to be hard to solve numerically because their solutions have regions of rapid variation. Extensive numerical experience has shown that it is important to consider the conditioning of such problems since algorithms are developed on the assumption that a small local error in the computed solution will produce a correspondingly small global error. This may be valid only if the problem is well conditioned. In this paper we describe how conditioning information can be added to state of the art codes, and give numerical results demonstrating the effectiveness of this approach.

Keywords: singular perturbation; two point boundary value problems; conditioning; local errors; deferred corrections.

DOI: 10.1504/IJCSM.2007.013763

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.1, pp.42 - 57

Published online: 25 May 2007 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article