Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations
This book describes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis li
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Springer-Verlag Berlin Heidelberg GmbH
Willem Hundsdorfer JanVerwer
Numerical Solution of Time-Dependent Advection-DiffusionReaction Equations
,
Springer
Willem Hundsdorfer JanVerwer Center for Mathematics and Computer Science (CWI) Kruislaan 413 1098 SJ Amsterdam The Netherlands e-mail: [email protected] [email protected]
Cataloging-in-Publication Data applied for A catalog record for this book is available from the library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
Mathematics Subject Classification (2000): 6SLOS,6SL06, 6SL20, 6SM06, 6SM12, 6SM20,6SM60
ISSN 0179-3632 ISBN 978-3-642-05707-6 ISBN 978-3-662-09017-6 (eBook) DOI 10.1007/978-3-662-09017-6 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
http://www.springer.de C Springer-Verlag Berlin Heidelberg 2003 Originally published by Springer-Verlag Berlin Heidelberg New York in 2003. Softcover reprint of the hardcover 1st edition 2003
The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: design&production, Heidelberg Typeset by the authors Printed on acid-free paper 46/3142LK-54321 0
Preface
This book deals with numerical methods for solving partial differential equations (PDEs) coupling advection, diffusion and reaction terms, with a focus on time-dependency. A combined treatment is presented of methods for hyperbolic problems, thereby emphasizing the one-way wave equation, methods for parabolic problems and methods for stiff and non-stiff ordinary differential equations (ODEs). With regard to time-dependency we have attempted to present the algorithms and the discussion of their properties for the three different types of differential equations in a unified way by using semi-discretizations, i.e., the method of lines, whereby the PDE is transformed into an ODE by a suitable spatial discretization. In addition, for hyperbolic problems we also discuss discretizations that use information based on characteristics. Due to this combination of methods, this book differs substantially from more specialized textbooks that deal exclusively with numerical methods for either PDEs or ODEs. We treat integration met
