An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems

Citation
Jr. Cash et al., An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems, ACM T MATH, 27(2), 2001, pp. 245-266
Citations number
23
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Science & Engineering
Journal title
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ISSN journal
0098-3500 → ACNP
Volume
27
Issue
2
Year of publication
2001
Pages
245 - 266
Database
ISI
SICI code
0098-3500(200106)27:2<245:AACSFT>2.0.ZU;2-J
Abstract
In a recent paper, the present authors derived an automatic continuation al gorithm for the solution of linear singular perturbation problems. The algo rithm was incorporated into two general-purpose codes for solving boundary value problems, and it was shown to deal effectively with a large test set of linear problems. The present paper describes how the continuation algori thm for linear problems can be extended to deal with the nonlinear case. Th e results of extensive numerical testing on a set of nonlinear singular per turbation problems are given, and these clearly demonstrate the efficacy of continuation for solving such problems.