John wiley sons interscience applied numerical methods using matlab apr 2005

APPLIED NUMERICAL METHODS USING MATLAB Won Young Yang Chung-Ang University, Korea Wenwu Cao Pennsylvania State University Tae-Sang Chung Chung-Ang University, Korea John Morris The University of Auckland, New Zealand A JOHN WILEY & SONS, INC., PUBLICATION APPLIED NUMERICAL METHODS USING MATLAB APPLIED NUMERICAL METHODS USING MATLAB Won Young Yang Chung-Ang University, Korea Wenwu Cao Pennsylvania State University Tae-Sang Chung Chung-Ang University, Korea John Morris The University of Auckland, New Zealand A JOHN WILEY & SONS, INC., PUBLICATION Questions about the contents of this book can be mailed to wyyang@cau.ac.kr MATLAB and Simulink are trademarks of the The MathWorks, Inc and are 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 and Simulink software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB and Simulink software Copyright  2005 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 www.copyright.com 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 authors 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 or extended by sales representatives or written sales materials The advice and strategies contained herein 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 within 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 Yang, Won-young, 1953– Applied numerical methods using MATLAB / Won Y Yang, Wenwu Cao, Tae S Chung, John Morris p cm Includes bibliographical references and index ISBN 0-471-69833-4 (cloth) Numerical analysis–Data processing MATLAB I Cao, Wenwu II Chung, Tae-sang, 1952– III Title QA297.Y36 2005 518–dc22 2004013108 Printed in the United States of America 10 To our parents and families who love and support us and to our teachers and students who enriched our knowledge CONTENTS Preface MATLAB Usage and Computational Errors xiii 1.1 Basic Operations of MATLAB / 1.1.1 Input/Output of Data from MATLAB Command Window / 1.1.2 Input/Output of Data Through Files / 1.1.3 Input/Output of Data Using Keyboard / 1.1.4 2-D Graphic Input/Output / 1.1.5 3-D Graphic Output / 10 1.1.6 Mathematical Functions / 10 1.1.7 Operations on Vectors and Matrices / 15 1.1.8 Random Number Generators / 22 1.1.9 Flow Control / 24 1.2 Computer Errors Versus Human Mistakes / 27 1.2.1 IEEE 64-bit Floating-Point Number Representation / 28 1.2.2 Various Kinds of Computing Errors / 31 1.2.3 Absolute/Relative Computing Errors / 33 1.2.4 Error Propagation / 33 1.2.5 Tips for Avoiding Large Errors / 34 1.3 Toward Good Program / 37 1.3.1 Nested Computing for Computational Efficiency / 37 1.3.2 Vector Operation Versus Loop Iteration / 39 1.3.3 Iterative Routine Versus Nested Routine / 40 1.3.4 To Avoid Runtime Error / 40 1.3.5 Parameter Sharing via Global Variables / 44 1.3.6 Parameter Passing Through Varargin / 45 1.3.7 Adaptive Input Argument List / 46 Problems / 46 vii MATLAB 495 If you use the MATLAB of version 5.x, you can refer to the usage of the constrained minimization routine ‘constr()’, which is summarized in the box below USAGE OF THE MATLAB 5.X BUILT-IN FUNCTION “CONSTR()” FOR CONSTRAINED OPTIMIZATION [x,options] = constr(’ftn’,x0,options,l,u) ž Input arguments (only ‘ftn’ and x0 required, the others optional) ‘ftn’ : usually defined in an m-file and should return two output arguments, one of which is a scalar value (f (x)) of the function (ftn) to be minimized and the other is a vector (g(x)) of constraints such that g(x) ≤ x0 : the initial guess of solution options: is used for setting the termination tolerance on x, f (x), and constraint violation through options(2)/(3)/(4), the number of the (leading) equality constraints among g(x) ≤ through options (13), etc (For more details, type ‘help foptions’ into the MATLAB command window) l,u : lower/upper bound vectors such that l ≤ x ≤ u ž Output arguments : minimum point reached in the permissible region satisfying the constraints options: outputs some information about the search process and the result like the function value at the minimum point (x) reached through options (8) x REFERENCES [B-1] Burden, Richard L., and Fairs, J Douglas, Numerical Analysis, 7th ed., Brooks/ Cole Thomson, Pacific Grove, CA, 2001 [B-2] Bell, H E., Gerschgorin’s theorem and the zeros of polynomials, Am Math Monthly 72, 292–295 (1965) [C-1] Canale, Raymond, and Chapra, Steven, Numerical Methods for Engineers: with Software and Programming Applications, McGraw-Hill, New York, 2002 [F-1] Fausett, L V., Applied Numerical Analysis Using MATLAB, Prentice-Hall, Upper Saddle River, NJ, 1999 [H-1] Hamming, R W., Numerical Methods for Scientists and Engineers, 2nd ed., McGraw-Hill, New York, 1973 [K-1] Kreyszig, Erwin, Advanced Engineering Mathematics, 8th ed., John Wiley & Sons, New York, 1999 [K-2] Kreyszig, Erwin, Introductory Functional Analysis with Applications, John Wiley & Sons, New York, 1978 [L-1] Lindfield, G R., and Peny, J E T., Numerical Methods Using MATLAB, 8th ed., Prentice-Hall, Upper Saddle River, NJ, 2000 [L-2] Luenberger, D G., Linear and Nonlinear Programming, 2nd ed., Addison-Wesley Publishing Company, Reading, MA, 1984 [M-1] Mathews, J H., and Fink, K D., Numerical Methods Using MATLAB, PrenticeHall, Upper Saddle River, NJ, 1999 [M-2] Maron, Melvin J., Numerical Analysis, Macmillan, Inc., New York, 1982 [N-1] Nakamura, Shoichiro, Numerical Analysis and Graphic Visualization with MATLAB, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 2002 [O-1] Oppenheim, Alan V., and Schafer, Ronald W., Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989 [P-1] Peaceman, D W., and Rachford, H H., The numerical solution of parabolic and elliptic differential equations, J Soc Ind Appl Math 3, 28–41 (1955) [P-2] Pham, D T., and Karaboga, D., Intelligent Optimization Techniques, SpringerVerlag, London, 1998 Applied Numerical Methods Using MATLAB, by Yang, Cao, Chung, and Morris Copyright  2005 John Wiley & Sons, Inc 497 498 REFERENCES [P-3] Phillips, C L., and Nagle, H T., Jr., Digital Control System Analysis and Design, Prentice-Hall, Upper Saddle River, NJ, 2002 [R-1] Rao, S S., The Finite Element Method in Engineering, 3rd ed., Butterworth Heinemann, Boston, 1999 [R-2] Recktenwald, G W., Numerical Methods with MATLAB, Prentice-Hall, Upper Saddle River, NJ, 2000 [S-1] Schilling, R J., and Harris, S L., Applied Numerical Methods for Engineers Using MATLAB and C, Brooks/Cole, Pacific Grove, CA, 2000 [S-2] Silvester, P P., and Ferrari, R L., Finite Elements for Electrical Engineers, 3rd ed., Cambridge University Press, Cambridge, U.K., 1996 [S-3] Stoer, J., and Bulirsch, R., Introduction to Numerical Analysis, Springer-Verlag, New York, 1980 [W-1] Website [W-2] Website [W-3] Website [W-4] Website