NUMERICALSOLUTIONOF ORDINARYDIFFERENTIAL …

NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

Kendall Atkinson, Weimin Han, David Stewart University of Iowa Iowa City, Iowa

A JOHN WILEY & SONS, INC., PUBLICATION

Copyright c 2009 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. 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, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at . Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created ore extended by sales representatives or written sales materials. The advice and strategies contained herin may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services please contact our Customer Care Department with the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572-4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format.

Library of Congress Cataloging-in-Publication Data:

Numerical Solution of Ordinary Differential Equations / Kendall E. Atkinson . . . [et al.]. p. cm.--(Wiley series in ???????)

"Wiley-Interscience." Includes bibliographical references and index. ISBN ????????????? (pbk.) 1. Numerical analysis. 2. Ordinary differential equations. I. Atkinson, Kendall E. II. Series.

MATLAB R is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book's use or discussion of MATLAB R software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB R software.

QA31.????.???? 2008 510.??????-??? Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1

To Alice, Huidi, and Sue

Preface

This book is an expanded version of supplementary notes that we used for a course on ordinary differential equations for upper-division undergraduate students and beginning graduate students in mathematics, engineering, and sciences. The book introduces the numerical analysis of differential equations, describing the mathematical background for understanding numerical methods and giving information on what to expect when using them. As a reason for studying numerical methods as a part of a more general course on differential equations, many of the basic ideas of the numerical analysis of differential equations are tied closely to theoretical behavior associated with the problem being solved. For example, the criteria for the stability of a numerical method is closely connected to the stability of the differential equation problem being solved.

This book can be used for a one-semester course on the numerical solution of differential equations, or it can be used as a supplementary text for a course on the theory and application of differential equations. In the latter case, we present more about numerical methods than would ordinarily be covered in a class on ordinary differential equations. This allows the instructor some latitude in choosing what to include, and it allows the students to read further into topics that may interest them. For example, the book discusses methods for solving differential algebraic equations (Chapter 10) and Volterra integral equations (Chapter 12), topics not commonly included in an introductory text on the numerical solution of differential equations.

vii

viii PREFACE

We also include MATLAB R programs to illustrate many of the ideas that are introduced in the text. Much is to be learned by experimenting with the numerical solution of differential equations. The programs in the book can be downloaded from the following website.



This site also contains graphical user interfaces for use in experimenting with Euler's method and the backward Euler method. These are to be used from within the framework of MATLAB.

Numerical methods vary in their behavior, and the many different types of differential equation problems affect the performance of numerical methods in a variety of ways. An excellent book for "real world" examples of solving differential equations is that of Shampine, Gladwell, and Thompson [74].

The authors would like to thank Olaf Hansen, California State University at San Marcos, for his comments on reading an early version of the book. We also express our appreciation to John Wiley Publishers.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download