Numerical Methods in Engineering With MATLAB

435 Pages·2005·2.24 MB·english

by  Jaan Kiusalaas

Numerical Methods in Engineering with MATLAB®
NumericalMethodsinEngineeringwithMATLAB®isatextforengineer-
ingstudentsandareferenceforpracticingengineers,especiallythose
whowishtoexplorethepowerandefficiencyofMATLAB.Thechoiceof
numericalmethodswasbasedontheirrelevancetoengineeringprob-
lems.Everymethodisdiscussedthoroughlyandillustratedwithprob-
lems involving both hand computation and programming. MATLAB
M-files accompany each method and are available on the book web
site.Thiscodeismadesimpleandeasytounderstandbyavoidingcom-
plexbook-keepingschemes,whilemaintainingtheessentialfeaturesof
themethod.MATLAB,waschosenastheexamplelanguagebecauseof
its ubiquitous use in engineering studies and practice. Moreover, it is
widelyavailabletostudentsonschoolnetworksandthroughinexpen-
siveeducationalversions.MATLABapopulartoolforteachingscientific
computation.
JaanKiusalaasisaProfessorEmeritusintheDepartmentofEngineering
Science and Mechanics at the Pennsylvania State University. He has
taughtnumericalmethods,includingfiniteelementandboundaryel-
ement methods for over 30 years. He is also the co-author of four
other Books—Engineering Mechanics: Statics, Engineering Mechanics:
Dynamics,MechanicsofMaterials,andanalternateversionofthiswork
withPythoncode.

NUMERICAL METHODS IN
ENGINEERING WITH
MATLAB®
Jaan Kiusalaas
ThePennsylvaniaStateUniversity
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge cb2 2ru, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521852883
©JaanKiusalaas2005
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2005
isbn-13 978-0-511-12811-0 eBook (NetLibrary)
isbn-10 0-511-12811-8 eBook (NetLibrary)
isbn-13 978-0-521-85288-3 hardback
isbn-10 0-521-85288-9 hardback
Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.
Contents
Preface.........vii
1.IntroductiontoMATLAB ............................. 1
2.SystemsofLinearAlgebraicEquations ............. 28
3.InterpolationandCurveFitting ..................... 103
4.RootsofEquations ...................................143
5.NumericalDifferentiation ........................... 182
6.NumericalIntegration ............................... 200
7.InitialValueProblems ............................... 251
8.Two-PointBoundaryValueProblems ............... 297
9.SymmetricMatrixEigenvalueProblems ............ 326
10.IntroductiontoOptimization ....................... 382
Appendices....411
Index...........421
v

Preface
This book is targeted primarily toward engineers and engineering students of ad-
vanced standing (sophomores, seniors and graduate students). Familiarity with a
computerlanguageisrequired;knowledgeofbasicengineeringsubjectsisuseful,but
notessential.
Thetextattemptstoplaceemphasisonnumericalmethods,notprogramming.
Mostengineersarenotprogrammers,butproblemsolvers.Theywanttoknowwhat
methodscanbeappliedtoagivenproblem,whataretheirstrengthsandpitfallsand
howtoimplementthem.Engineersarenotexpectedtowritecomputercodeforbasic
tasksfromscratch;theyaremorelikelytoutilizefunctionsandsubroutinesthathave
beenalreadywrittenandtested.Thusprogrammingbyengineersislargelyconfined
toassemblingexistingpiecesofcodeintoacoherentpackagethatsolvestheproblem
athand.
The“piece”ofcodeisusuallyafunctionthatimplementsaspecifictask.Forthe
userthedetailsofthecodeareunimportant.Whatmattersistheinterface(whatgoes
inandwhatcomesout)andanunderstandingofthemethodonwhichthealgorithm
isbased.Sincenonumericalalgorithmisinfallible,theimportanceofunderstanding
theunderlyingmethodcannotbeoveremphasized;itis,infact,therationalebehind
learningnumericalmethods.
This book attempts to conform to the views outlined above. Each numerical
method is explained in detail and its shortcomings are pointed out. The examples
thatfollowindividualtopicsfallintotwocategories:handcomputationsthatillustrate
theinnerworkingsofthemethod,andsmallprogramsthatshowhowthecomputer
codeisutilizedinsolvingaproblem.Problemsthatrequireprogrammingaremarked
with(cid:1).
The material consists of the usual topics covered in an engineering course on
numericalmethods:solutionofequations,interpolationanddatafitting,numerical
differentiationandintegration,solutionofordinarydifferentialequationsandeigen-
valueproblems.Thechoiceofmethodswithineachtopicistiltedtowardrelevance
vii
viii Preface
toengineeringproblems.Forexample,thereisanextensivediscussionofsymmetric,
sparsely populated coefficient matrices in the solution of simultaneous equations.
Inthesamevein,thesolutionofeigenvalueproblemsconcentratesonmethodsthat
efficientlyextractspecificeigenvaluesfrombandedmatrices.
Animportantcriterionusedintheselectionofmethodswasclarity.Algorithms
requiringoverlycomplexbookkeepingwererejectedregardlessoftheirefficiencyand
robustness.Thisdecision,whichwastakenwithgreatreluctance,isinkeepingwith
theintenttoavoidemphasisonprogramming.
The selection of algorithms was also influenced by current practice. This dis-
qualifiedseveralwell-knownhistoricalmethodsthathavebeenovertakenbymore
recentdevelopments.Forexample,thesecantmethodforfindingrootsofequations
wasomittedashavingnoadvantagesoverBrent’smethod.Forthesamereason,the
multistepmethodsusedtosolvedifferentialequations(e.g.,MilneandAdamsmeth-
ods)wereleftoutinfavoroftheadaptiveRunge–KuttaandBulirsch–Stoermethods.
Notablyabsentisachapteronpartialdifferentialequations.Itwasfeltthatthis
topicisbesttreatedbyfiniteelementorboundaryelementmethods,whichareoutside
thescopeofthisbook.Thefinitedifferencemodel,whichiscommonlyintroduced
in numerical methods texts, is just too impractical in handling multidimensional
boundaryvalueproblems.
Asusual,thebookcontainsmorematerialthancanbecoveredinathree-credit
course.Thetopicsthatcanbeskippedwithoutlossofcontinuityaretaggedwithan
asterisk(*).
The programs listed in this book were tested with MATLAB® 6.5.0 and under
Windows®XP.Thesourcecodecanbedownloadedfromthebook’swebsiteat
www.cambridge.org/0521852889
The author wishes to express his gratitude to the anonymous reviewers and
Professor Andrew Pytel for their suggestions for improving the manuscript. Credit
isalsoduetotheauthorsofNumericalRecipes(CambridgeUniversityPress)whose
presentationofnumericalmethodswasinspirationalinwritingthisbook.
1 Introduction to MATLAB
1.1 General Information
Quick Overview
(cid:1)
R
ThischapterisnotintendedtobeacomprehensivemanualofMATLAB .Oursole
aimistoprovidesufficientinformationtogiveyouagoodstart.Ifyouarefamiliar
withanothercomputerlanguage,andweassumethatyouare,itisnotdifficulttopick
uptherestasyougo.
MATLABisahigh-levelcomputerlanguageforscientificcomputinganddatavi-
sualizationbuiltaroundaninteractiveprogrammingenvironment.Itisbecomingthe
premiereplatformforscientificcomputingateducationalinstitutionsandresearch
establishments.Thegreatadvantageofaninteractivesystemisthatprogramscanbe
testedanddebuggedquickly,allowingtheusertoconcentratemoreontheprinciples
behindtheprogramandlessonprogrammingitself.Sincethereisnoneedtocom-
pile,linkandexecuteaftereachcorrection,MATLABprogramscanbedevelopedin
muchshortertimethanequivalentFORTRANorCprograms.Onthenegativeside,
MATLABdoesnotproducestand-aloneapplications—theprogramscanberunonly
oncomputersthathaveMATLABinstalled.
MATLAB has other advantages over mainstream languages that contribute to
rapidprogramdevelopment:
(cid:1)
MATLABcontainsalargenumberoffunctionsthataccessprovennumericalli-
braries,suchasLINPACKandEISPACK.Thismeansthatmanycommontasks(e.g.,
solutionofsimultaneousequations)canbeaccomplishedwithasinglefunction
call.
(cid:1)
Thereisextensivegraphicssupportthatallowstheresultsofcomputationstobe
plottedwithafewstatements.
(cid:1)
Allnumericalobjectsaretreatedasdouble-precisionarrays.Thusthereisnoneed
todeclaredatatypesandcarryouttypeconversions.
1