Numerical Methods for Engineering Applications

by
Edition: 2nd
Format: Hardcover
Pub. Date: 1998-04-17
Publisher(s): Wiley-Interscience
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $215.41

Buy New

Usually Ships in 8 - 10 Business Days.
$215.33

Rent Textbook

Select for Price
There was a problem. Please try again later.

Used Textbook

We're Sorry
Sold Out

eTextbook

We're Sorry
Not Available

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

State-of-the-art numerical methods for solving complex engineering problems Great strides in computer technology have been made in the years since the popular first edition of this book was published. Several excellent software packages now help engineers solve complex problems. Making the most of these programs requires a working knowledge of the numerical methods on which the programs are based. Numerical Methods for Engineering Application provides that knowledge. While it avoids intense mathematical detail, Numerical Methods for Engineering Application supplies more in-depth explanations of methods than found in the typical engineer's numerical "cookbook." It offers complete coverage of most commonly encountered algebraic, interpolation, and integration problems. Ordinary differential equations are examined in great detail, as are three common types of partial differential equations--parabolic, elliptic, and hyperbolic. The author also explores a wide range of methods for solving initial and boundary value problems. This complete guide to numerical methods for solving engineering problems on computers provides: * Practical advice on how to select the best method for a given problem * Valuable insights into how each method works and why it is the best choice * Complete algorithms and source code for all programs covered * Code from the book and problem-solving programs designed by the author available from the author's website Numerical Methods for Engineering Application is a valuable working resource for engineers and applied physicists. It also serves as an excellent upper-level text for physics and engineering students in courses on modern numerical methods.

Author Biography

JOEL H. FERZIGER, PhD, is a professor in the Stanford University Department of Mechanical Engineering. Dr. Ferziger holds a doctorate in nuclear engineering from the University of Michigan. He is a Max Planck Award recipient, a Humboldt Fellow, and a Fellow of ASME and APS. His other books include Computational Methods for Fluid Dynamics.

Table of Contents

PREFACE TO THE SECOND EDITION xi(4)
PREFACE TO THE FIRST EDITION xv
1. SHORT REVIEW OF LINEAR ALGEBRA
1(13)
1.1. Introduction and Notation
1(2)
1.2. Gauss Elimination and LU Decomposition
3(4)
1.3. Tridiagonal and Other Banded Systems
7(2)
1.4. Block Systems
9(2)
1.5. Eigenvalues
11(3)
2. INTERPOLATION
14(29)
2.1. Lagrange Interpolation
15(12)
2.1.1. Theory
15(2)
2.1.2. Error Analysis
17(1)
2.1.3. Divided Differences
18(1)
2.1.4. Examples
19(5)
2.1.5. Piecewise Polynomial Interpolation
24(2)
2.1.6. Summary
26(1)
2.2. Hermite Interpolation
27(1)
2.3. Splines
28(9)
2.3.1. Definition and Development
28(4)
2.3.2. Examples and Programs
32(3)
2.3.3. B-Splines
35(1)
2.3.4. Final Remarks
36(1)
2.4. Tension Splines
37(1)
2.5. Parametric and Multidimensional Interpolation-Computer Graphics
38(3)
2.5.1. Parametric Interpolation
39(1)
2.5.2. Multidimensional Interpolation
40(1)
2.5.3. Graphics and Design
40(1)
Problems
41(2)
3. INTEGRATION
43(32)
3.1. Newton-Cotes Formulas
45(5)
3.2. Richardson Extrapolation and Error Estimation
50(3)
3.3. Romberg Integration
53(4)
3.4. Adaptive Quadrature
57(8)
3.5. Gauss Quadrature
65(5)
3.6. Monte Carlo Methods
70(2)
3.7. Singularities
72(1)
3.7.1. Integration by Parts
72(1)
3.7.2. Singularity Subtraction
72(1)
3.8. Concluding Remarks
73(1)
Problems
73(2)
4. ORDINARY DIFFERENTIAL EQUATIONS: I. INITIAL VALUE PROBLEMS
75(63)
4.1. Numerical Differentiation
77(9)
4.1.1. Interpolation
77(4)
4.1.2. Taylor Series
81(4)
4.1.3. Numerical Integration
85(1)
4.2. Nonuniform Grids
86(1)
4.3. Euler Explicit Method
87(3)
4.4. Stability
90(10)
4.5. Backward or Implicit Euler Method
100(3)
4.6. Error Estimation and Accuracy Improvement
103(6)
4.6.1. Error Estimation
104(1)
4.6.2. Richardson Extrapolation
105(1)
4.6.3. Trapezoid Rule
106(2)
4.6.4. Other Approaches
108(1)
4.7. Predictor-Corrector Methods
109(2)
4.8. Runge-Kutta Methods
111(5)
4.9. Multistep Methods
116(7)
4.10. Choice of Method: Automatic Error Control
123(1)
4.11. Systems of Equations-Stiffness
124(9)
4.11.1. Treatment of Systems of Ordinary Differential Equations
124(1)
4.11.2. Stiffness
125(2)
4.11.3. Numerical Methods for Stiff Problems
127(4)
4.11.4. Splitting Methods
131(2)
4.11.5. Variable-Step-Size Methods
133(1)
4.12. Inherent Instability
133(1)
4.13. Growing Solutions
134(1)
Problems
134(4)
5. ORDINARY DIFFERENTIAL EQUATIONS: II. BOUNDARY VALUE PROBLEMS
138(44)
5.1. Shooting
139(11)
5.2. Direct Methods: Introduction
150(5)
5.3. Higher-Order Direct Methods
155(4)
5.4. Compact Methods
159(2)
5.5. Nonuniform Grids
161(5)
5.5.1. Finite Difference Approximations
162(1)
5.5.2. Coordinate Transformations
163(3)
5.6. Finite Element Methods
166(3)
5.7. Adaptive Grids
169(3)
5.8. Eigenvalue Problems
172(8)
5.8.1. Direct Methods
174(4)
5.8.2. Shooting Methods
178(2)
Problems
180(2)
6. PARTIAL DIFFERENTIAL EQUATIONS: I. PARABOLIC EQUATIONS
182(46)
6.1. Classification of Partial Differential Equations
183(4)
6.1.1. Characteristics
183(4)
6.2. Explicit Methods
187(9)
6.3. Crank-Nicolson Method
196(6)
6.4. Dufort-Frankel Method
202(3)
6.5. Keller Box Method
205(2)
6.6. Second-Order Backward Method
207(1)
6.7. Higher-Order Methods
208(2)
6.8. Two and Three Spatial Dimensions: Alternating Direction Implicit Methods
210(10)
6.8.1. Heat Equation in Two Dimensions
210(3)
6.8.2. Peaceman-Rachford Method
213(2)
6.8.3. Approximate Factorization
215(2)
6.8.4. Other Splitting Methods
217(3)
6.9. Other Coordinate Systems
220(4)
6.10. Nonlinear Problems
224(2)
6.11. Final Remarks-Other Methods
226(1)
Problems
226(2)
7. PARTIAL DIFFERENTIAL EQUATIONS: II. ELLIPTIC EQUATIONS
228(88)
7.1. Discretization
229(8)
7.1.1. Finite Differences
229(3)
7.1.2. Finite Volume Approximations
232(2)
7.1.3. Boundary Conditions
234(1)
7.1.4. System of Equations
235(2)
7.1.5. Complex Geometry
237(1)
7.2. Introduction to Iterative Methods and Their Properties
237(7)
7.2.1. Construction of Iterative Methods
237(2)
7.2.2. Errors in Iterative Methods
239(1)
7.2.3. Convergence Error
240(1)
7.2.4. Stopping Criterion
241(2)
7.2.5. Estimation of Discretization Error
243(1)
7.3. Jacobi Iteration
244(6)
7.3.1. The Method
244(1)
7.3.2. Convergence
244(1)
7.3.3. Connection to Heat Equation
245(1)
7.3.4. Other Equations
246(4)
7.4. Gauss-Seidel Method
250(3)
7.5. Line Relaxation Method
253(1)
7.6. Successive Overrelaxation
254(9)
7.6.1. Extrapolation
255(2)
7.6.2. Point Successive Overrelaxation
257(4)
7.6.3. Successive Line Overrelaxation
261(2)
7.7. Alternating Direction Implicit Methods
263(5)
7.8. Incomplete LU Decomposition: Stone's Method
268(5)
7.9. Methods for Parallel Computers
273(3)
7.9.1. Red-Black Gauss-Seidel Method
274(2)
7.9.2. Parallelization of Other Methods
276(1)
7.10. Multigrid Methods
276(7)
7.11. Conjugate Gradient Methods
283(7)
7.11.1. Concept
283(2)
7.11.2. Preconditioning
285(1)
7.11.3. Biconjugate Gradients and CGSTAB
286(4)
7.12. Adaptive Grids
290(2)
7.13. Finite Element Methods
292(5)
7.14. Discrete Fourier Transforms
297(9)
7.14.1. Review of Fourier Series
297(2)
7.14.2. Discrete Fourier Series
299(3)
7.14.3. Spectral Differentiation
302(1)
7.14.4. Fast Fourier Transform
303(3)
7.15. Fourier or Spectral Methods
306(2)
7.16. Boundary Integral Methods
308(3)
7.17. Finite Differences in Complex Geometry
311(2)
Problems
313(3)
8. PARTIAL DIFFERENTIAL EQUATIONS: III. HYPERBOLIC EQUATIONS
316(47)
8.1. Review of Theory
317(8)
8.1.1. Quasi-Linear First-Order Equations
317(1)
8.1.2. Characteristics of Second-Order Equations
318(4)
8.1.3. Nonlinear Equations and Shocks
322(3)
8.2. Method of Characteristics
325(15)
8.2.1. First-Order Equations
325(2)
8.2.2. Second-Order Equations
327(10)
8.2.3. Method of Characteristics on Cartesian Grids
337(3)
8.3. Explicit Methods
340(8)
8.3.1. Explicit Central Difference Methods
341(2)
8.3.2. Upwind Methods
343(2)
8.3.3. Lax-Wendroff Method
345(3)
8.4. Implicit Methods
348(4)
8.5. Splitting Methods
352(9)
8.5.1. Explicit Split Methods
353(1)
8.5.2. Convection in Two Dimensions
354(6)
8.5.3. Implicit Split Methods
360(1)
Problems
361(2)
APPENDIX A: LIST OF COMPUTER CODES 363(3)
APPENDIX B: ANNOTATED BIBLIOGRAPHY 366(5)
APPENDIX C: NOTE ON THE NEWTON-RAPHSON METHOD 371(2)
INDEX 373

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.