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From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: * "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers equally finite difference and finite element methods."-Burrelle's. * "The authors have selected an elementary (but not simplistic) mode of presentation. Many different computational schemes are described in great detail . . . Numerous practical examples and applications are described from beginning to the end, often with calculated results given."-Mathematics of Computing. * "This volume . . . devotes its considerable number of pages to lucid developments of the methods [for solving partial differential equations] . . . the writing is very polished and I found it a pleasure to read!"-Mathematics of Computation Of related interest . . .NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen and Eli L. Isaacson. A modern, practical look at numerical analysis, this book guides readers through a broad selection of numerical methods, implementation, and basic theoretical results, with an emphasis on methods used in scientific computation involving differential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan. Presenting an easily accessible treatment of mathematical methods for scientists and engineers, this acclaimed work covers fluid mechanics and calculus of variations as well as more modern methods-dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. 1996 (0-471-16513-1) 496 pp.
E-Book Content
NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS IN SCIENCE AND ENGINEERING
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NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS IN SCIENCE AND ENGINEERING
LEON LAPIDUS G E O R G E F. P I N D E R
University of Vermont
A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York · Chichester · Weinheim · Brisbane · Singapore · Toronto
This text is printed on acid-free paper. ® Copyright Ο 1999 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ @ WILEY.COM. For ordering and customer service, call 1-800-CALL-WILEY. Library of Congress Cataloging in Publication Data: Lapidus, Leon. Numerical solution of partial differential equations in science and engineering. "A Wiley-Interscience publication." Includes index. 1. Science—Mathematics. 2. Engineering. mathematics. 3. Differential equations, Partial— Numerical solutions. I. Pinder, George Francis, 1942II. Title. Q172.L36 515.3'53 81-16491 ISBN 0-471-09866-3 AACR2 ISBN 0-471-35944-0 (paperback) 10 9 8 7 6 5 4 3
Preface
This book was written to provide a text for graduate and undergraduate students who took our courses in numerical methods. It incorporates the essential elements of all the numerical methods currently used extensively in the solution of partial differential equations encountered regularly in science and engineering. Because our courses were typically populated by students from varied backgrounds and with