Numerical Methods for Singularly Perturbed Differential Equations Co
This book collects, explains and analyses basic methods and recent results for the successful numerical solution of singularly perturbed differential equations. Such equations model many physical phenomena and their solutions are characterized by the pres
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Editorial Board R. L. Graham, Murray Hili (NJ) J. Stoer, Würzburg R. Varga, Kent (Ohio)
Springer-Verlag Berlin Heidelberg GmbH
H.-G. Hoos M. Stynes L.Tabiska
Numerical Methods tor Singularly Perturbed Differential Equations Convection-Diffusion and Flow Problems
Springer
Hans-Görg Roos Institut für Numerische Mathematik Technische Universität Dresden Zellescher Weg 12-14 0-01062 Dresden Germany e-mail: roos@math .tu-dresden.de Martin Stynes Department of Mathematics University College Cork Cork Ireland e-mail: [email protected] Lutz Tobiska Institut für Analysis und Numerik Otto-von-Guericke Universität Magdeburg Postfach 4120 0-39016 Magdeburg Germany e-mail: [email protected] Catalcg ing-in-Publ ication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Roos, Hans-Görg: Nume rica\ meth ods for singularly perturbed diff erential equat io ns : con vecti on diffus ion and flow pr obl ems / H .-G . Roos ; M. Stynes ; L. Tob is ka. - Berlin ; Heide1berg ; New York ; Barcelona ; Budapest ; Hon g Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer. 1996 (Spri nger serie s in com putat iona l rnathemarlcs : 24)
.'!E: Stynes , Mart in :; Tob iska, Lutz r: GT
Mathematics Subject Classification (1991): 65Lxx, 65Mxx, 65Nxx, 76D05, 76Mxx ISBN 978-3-662-03208-4 ISBN 978-3-662-03206-0 (eBook) DOI 10.1007/978-3-662-03206-0 This work is subject to copyr ight. All rights are reserved , whether the whole or part 01the material is concerned, specilically the rights 01translat lon, reprinting , reuse 01illustratlons , recitation , broadcast ing, reproduct ion on microlilm or in any other way, and storage in data banks . Duplication 01this publicat ion or parts thereol is permitted only unde r the prov isions 01the German Copy right Law 01September 9, 1965, in its current vers ion , and perm ission lor use must always be obta ined Irom Springer -Verlag . Violations are liable lor prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1996 Originally published by Springer-Verlag Berlin Heidelberg New York in 1996. Softcover reprint of the hardcover 1st edition 1996
Typesettin g: Camera-ready copy from the autho rs using a Springer TEX macro package SPIN: 10100153 41/3143 - 5432 1 0 - Printed on acid-free paper
Preface
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic expansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless , asymptotic expansions may be impossible to construct or may fail to simplify the given problem ; then numerical approximations are often the only option . The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been st eadily pushed back , the exposition of new developments in the analysis
