with FORTRAN, QuickBASIC, MATLAB, and Mathematica

354 Pages·2003·4.23 MB·English

Engineering
Analysis
Interactive Methods and Programs
with FORTRAN, QuickBASIC, MATLAB,
and Mathematica
Y. C. Pao
CRC Press
Boca Raton London New York Washington, D.C.
© 2001 by CRC Press LLC
Acquiring Editor: Cindy Renee Carelli
Project Editor: Albert W. Starkweather, Jr.
Cover design: Dawn Boyd
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© 1999 by CRC Press LLC
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© 2001 by CRC Press LLC
Files Available from CRC Press
FORTRAN, QuickBASIC, MATLAB, and Mathematic files, which contain the
source and executable programs associated with this book are available from CRC
Press’ website — http://www.crcpress.com.
Before downloading, prepare two 3.5-inch, high-density disks — one for the
files and one for a backup. Also create a temporary directory named <interactive>
on your hard drive, which will expedite downloading. To download these files, type:
http://www.crcpress.com/us/ElectronicProducts/downandup.asp .(cid:13)W(cid:10) hen prompted, enter
2016 under name and crcpress under password. Then store the files in the
<interactive> folder. If you encounter a problem, call 1-800-CRC-PRES (272-7737).
The dowloaded files may be copied to a 3.5-inch disk. The temporary <interactive>
folder then may be deleted. Don’t forget to make a backup copy of your 3.5-inch disk.
There are four subdirectories <FORTRAN>, <QB>, <mFiles>, and <Math-
tica> which contain the FORTRAN source and executable programs, QuickBASIC
source and executable programs, m files of MATLAB, and input and output state-
ments of for the Mathematica operations depicted in this textbook, respectively:
1. <FORTRAN> has the following files:
Bairstow.FOR CharacEquationFOR CubeSpln.FOR DiffTabl.FOR
EditFOR.EXE EigenVec.FOR EigenvIt.FOR ExactFit.FOR
FindRoot.FOR FOR1.EXE FOR2.EXE FORTRAN.LIB
Gauss.FOR GauJor.FOR LagrangI.FOR LeastSq1.FOR
LeastSqG.FOR LINK.EXE MatxInvD.FOR NewRaphG.FOR
NuIntgra.FOR OdeBvpFD.FOR OdeBvpRK.FOR ParabPDE.FOR
Relaxatn.FOR RungeKut.FOR Volume.FOR WavePDE.FOR
EDITFOR.EXE is provided for re-editing the *.FOR source programs such as
Bairstow.FOR, CubeSpln.FOR, etc. (refer to the FORTRAN programs index) to
include supplementary subprograms describing the problem which need to be solved
interactively. To re-edit, insert the 3.5-inch disk into Drive A and when the a:\ prompt
shows, type cd fortran to switch to the <FORTRAN> subdirectory. For example,
to solve a polynomial by the Bairstow’s method one needs to define the polynomial,
for which the roots are to be computed. To reedit Bairstow.FOR, the user enters
a:\editfor Bairstow.for to add new FORTRAN statements or change them. Notice
that both upper and lower case characters are acceptable. While creating a new
version of Bairstow.FOR, the old version will be saved in Bairstow.BAK.
To create an object file, FOR1 filename such as Bairstow.FOR and FOR2 need
to be implemented. A BAISTOW.OBJ will then be generated. For linking with the
FORTRAN library functions, FORTRAN.LIB, one enters, for example, LINK
Bairstow to create an executable file Bairstow.EXE. To run, the user simply types
Bairstow after the prompt A:\ and then answers questions interactively.
© 2001 by CRC Press LLC
2. <QuickBASIC> has the following files:
Select.BAS Select.EXE
Bairstow.EXE BRUN40.EXE CharacEq.EXE CubeSpln.EXE
EigenStb.EXE EigenVec.EXE EigenVib.EXE EigenvIt.EXE
ExactFit.EXE FindRoot.EXE Gauss.EXE LagrangI.EXE
LeastSq1.EXE LeastSqG.EXE MatxInvD.EXE NuIntgra.EXE
OdeBvpFD.EXE OdeBvpRK.EXE ParabPDE.EXE QB.EXE
Relaxatn.EXE RungeKut.EXE Volume.EXE
Bairstow.QB CharacEq.QB CubeSpln.QB DiffTabl.QB
EigenStb.QB EigenVec.QB EigenVib.QB EigenvIt.QB
ExactFit.QB FindRoot.QB GauJor.QB Gauss.QB
LagrangI.QB LeastSq1.QB LeastSqG.QB MatxAlgb.QB
MatxMtpy.QB NewRaphG.QB NuIntgra.QB OdeBvpFD.QB
OdeBvpRK.QB ParabPDE.QB Relaxatn.QB RungeKut.QB
Volume.QB WavePDE.QB
To commence QuickBASIC, when a:\ is prompted on screen, the user enters
QB. QB.EXE and BRUN40.EXE therefore are included in <QB>. The program
Select enables user to select the available QuickBASIC program in this textbook.
After user responds with C:\Select, the screen shows a menu as shown in Figure 1
and user then follow the screen help-messages to run a desired program.
3. <mFiles> is a subdirectory associated with MATLAB and has the following
files:
BVPF.m DerivatF.m DiffTabl.m EigenvIt.m
F.m FindRoot.m FP.m Functns.m
FuncZ.m FuncZnew.m FunF.m GauJor.m
integrnd.m LagrangI.m LeastSqG.m NewRaphG.m
ParabPDE.m Relaxatn.m Volume.m Warping.m
WavePDE.m
When the 3.5-inch disk containing all of these m files is in Drive A, any of these
files can be accessed by enclosing the filename inside a pair of parentheses as
illustrated in Section 3.2 where F.m and FP.m are required for FindRoot.m and in
Section 5.2 where an integrand function integrnd.m is defined for numerical inte-
gration. If all files have been added into MATLAB library m files, then no reference
to the Drive A is necessary and the pair of parentheses can also be dropped.
4. <Mathtica> is a subdirectory associated with Mathematica and has the files of:
Bairstow.MTK CubeSpln.MTK DiffTabl.MTK EigenVec.MTK
ExactFit.MTK FindRoot.MTK FUNCTNS.MTK EigenvIt.MTK
Gauss.MTK GauJor.MTK LagrangI.MTK LeastSq1.MTK
LeastSqG.MTK MatxAlgb.MTK NewRaphG.MTK NuIntgra.MTK
OdeBvpFD.MTK OdeBvpRK.MTK ParabPDE.MTK Rexalatn.MTK
RungeKut.MTK Volume.MTK WavePDE.MTK
© 2001 by CRC Press LLC
Any of the above programs can be executed by Mathematica via mouse oper-
ation. First, by clicking the File option and when the pull-down menu appears, select
Open and then enter the filename such as a:\Mathtica\MatxAlgb.MTK (assuming
the 3.5-inch disk containing <Mathtica> is in Drive A) and press the Enter key.
When all lines of this file is displayed on screen, move cursor to any input line such
as In[1]: A = {{1,2},{3,4}}; MatrixForm[A] and hit the Enter key. Mathematica
will respond by repeating those lines for Out[1]. Hence, user can reproduce all of
the output lines by sequentially running the input lines [1] through [9]. However, if
user first run In[1] and then In[3], Mathematica cannot perform the addition of [A]
because [B] is not defined. If after having run In[1], user selects In[5], or, In[6],
Mathematica then has no problem of giving out results.
FIGURE 1. The Select screen.
© 2001 by CRC Press LLC
Dedication
This book is dedicated to Prof. E. J. Marmo,
who offered a congenial work-environment for the author
to grow in the computer-aided engineering field.
© 2001 by CRC Press LLC
Preface and Acknowledgments
Writing textbooks on topics in the field of Computer Aided Engineering (CAE)
indeed has been a very satisfying experience. First, I had the pleasure of being a
coauthor with Prof. Thomas C. Smith of the book Introduction to Digital Computer
Plotting by Gordon & Breach in 1973. The book Elements of Computer-Aided
Design and Manufacturing, CAD/CAM, was published in 1982 by John Wiley &
Sons. The book A First Course in Finite Element Analysis published by Allyn &
Bacon followed in 1986, and Engineering Drafting and Solid Modeling with Silver-
Screen, published by CRC Press, appeared in 1993.
Having taught the subjects of computer methods for engineering analysis since
1966, I finally have the courage to organize this textbook out of a large volume of
classroom notes collected over the past 31 years.
The rapid growth of computer technology is difficult for any one to keep pace,
and to make revision of textbooks in the CAE field. However, the computational
methods developed by the pioneers, such as Euler, Gauss, Lagrange, Newton, and
Runge, continue to serve us incredibly effective. These computational algorithms
remain classic, only are now executed with modern computer technology.
As far as the programming languages are concerned, FORTRAN has been
dominating the scientific fields for many decades. BASIC considered by many to
be too plain and cumbersome while C is considered by others to be too sophisticated;
both, however, are gaining popularity and increasingly replacing FORTRAN in the
computational community. This is particularly true when QuickBASIC was intro-
duced by Microsoft.
MATLAB and Mathematica developed by the MathWorks, Inc. and Wolfram
Research, Inc., respectively both contain a vast collection of files (similar to FOR-
TRAN’s library functions) which can perform the often-encountered computational
problems. For implementation, the MATLAB and Mathematica instructions to be
interactively entered through keyboard are extremely simple. And, it also provides
very easy-to-use graphic output. When students find it too easy to use, they often
become uninterested in learning what are the methods involved. This text is prepared
with FORTRAN, QuickBASIC, MATLAB and Mathematica, and more impor-
tantly gives the algorithms involved in the methods. Ample number of sample
problems are solved to demonstrate how the developed programs should be inter-
actively applied. Furthermore, the development of the user-generated supplementary
files is emphasized so that more supporting subprograms can be added to the
MATLAB m-files and Mathematica toolkits. It is a text for self-study as well as
for the need of general references.
Numerous friends, colleagues, and students have assisted in collecting the materials
assembled herein, and they have made a great number of constructive suggestions for
the betterment of this work. To them, I am most grateful. Especially, I would like to
© 2001 by CRC Press LLC
thank my long-time friends Dr. H. C. Wang, formerly with the IBM Thomas Watson
Research Laboratory and now with the Industrial Research Institutes in Hsingchu,
Taiwan; Dr. Erik L. Ritman of the Mayo Clinic in Rochester, MN, and Leon Hill
of the Boeing Company in Seattle, WA, for their help and encouragement throughout
my career in the CAE field. Profs. R. T. DeLorm, L. Kersten, C. W. Martin, R. N.
McDougal, G. M. Smith, and E. J. Marmo had assisted in acquiring equipment and
research funds which made my development in the CAE field possible, I extend my
most sincere gratitude to these colleagues at the University of Nebraska–Lincoln.
For providing constructive inputs to my published works, I should give credits to
Prof. Gary L. Kinzel of the Ohio State University, Prof. Donald R. Riley of the
University of Minnesota, Dr. L. C. Chang of the General Motors’ EDS Division, Dr.
M. Maheshiwari and Mr. Steve Zitek of the Brunswick Corp., my former graduate
assistants J. Nikkola, T. A. Huang, K. A. Peterson, Dr. W. T. Kao, Dr. David S. S.
Shy, C. M. Lin, R. M. Sedlacek, L. Shi, J. D. Wilson, Dr. A. J. Wang, Dave Breiner,
Q. W. Dong, and Michael Newman, and former students Jeff D. Geiger, Tim Car-
rizales, Krishna Pendyala, S. Ravikoti, and Mark Smith. I should also express my
appreciation to the readers of my other four textbooks mentioned above who have
frequently contacted me and provided input regarding various topics that they would
like to be considered as connected to the field of CAE and numerical problems that
they would like to be solved by application of computer. Such input has proven to
be invaluable to me in preparation of this text. CRC Press has been a delightful
partner in publishing my previous book and again this book. The completion of this
book would not be possible without the diligent effort and superb coordination of
Cindy Renee Carelli, Suzanne Lassandro, and Albert Starkweather, I wish to express
my deepest appreciation to them and to the other CRC editorial members. Last but
not least, I thank my wife, Rosaline, for her patience and encouragement.
Y. C. Pao
© 2001 by CRC Press LLC
Contents
1 Matrix Algebra and Solution of Matrix Equations
1.1 Introduction
1.2 Manipulation of Matrices
1.3 Solution of Matrix Equation
1.4 Program Gauss — Gaussian Elimination Method
1.5 Matrix Inversion, Determinant, and Program MatxInvD
1.6 Problems
1.7 Reference
2 Exact, Least-Squares, and Spline Curve-Fits
2.1 Introduction
2.2 Exact Curve Fit
2.3 Program LeastSq1 — Linear Least-Squares Curve-Fit
2.4 Program LeastSqG — Generalized Least-Squares Curve-Fit
2.5 Program CubeSpln — Curve Fitting with Cubic Spline
2.6 Problems
2.7 Reference
3 Roots of Polynomial and Transcendental Equations
3.1 Introduction
3.2 Iterative Methods and Program Roots
3.3 Program NewRaphG — Generalized Newton-Raphson
Iterative Method
3.4 Program Bairstow — Bairstow Method for Finding
Polynomial Roots
3.5 Problems
3.6 References
4 Finite Differences, Interpolation, and Numerical Differentiation
4.1 Introduction
4.2 Finite Differences and Program DiffTabl — Constructing
Difference Table
4.3 Program LagrangI — Applications of Lagrangian
Interpolation Formula
4.4 Problems
4.5. Reference
5 Numerical Integration and Program Volume
5.1 Introduction
5.2 Program NuIntGra — Numerical Integration by Application of the
Trapezoidal and Simpson Rules
© 2001 by CRC Press LLC
5.3 Program Volume — Numerical Solution of Double Integral
5.4 Problems
5.5 References
6 Ordinary Differential Equations — Initial and Boundary
Value Problems
6.1 Introduction
6.2 Program RungeKut — Application of Runge-Kutta Method
for Solving InitialValue Problems
6.3 Program OdeBvpRK — Application of Runge-Kutta Method
for Solving Boundary Value Problems
6.4 Program OdeBvpFD — Application of Finite-Difference Method
for Solving Boundary-Value Problems
6.5 Problems
6.6 References
7 Eigenvalue and Eigenvector Problems
7.1 Introduction
7.2 Programs EigenODE.Stb and EigenODE.Vib — for Solving
Stability and Vibration Problems
7.3 Program CharacEq — Derivation of Characteristic Equation
of a Specified Square Matrix
7.4 Program EigenVec — Solving Eigenvector by Gaussian
Elimination Method
7.5 Program EigenvIt — Iterative Solution of Eigenvalue
and Eigenvector
7.6 Problems
7.7 References
8 Partial Differential Equations
8.1 Introduction
8.2 Program ParabPDE — Numerical Solution of Parabolic Partial
Differential Equations
8.3 Program Relaxatn — Solving Elliptical Partial Differential
Equations by Relaxation Method
8.4 Program WavePDE — Numerical Solution of Wave Problems
Governed by Hyperbolic Partial Differential Equations
8.5 Problems
8.6 References
© 2001 by CRC Press LLC