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El. knyga: Fundamentals of Engineering Numerical Analysis

  • Formatas: PDF+DRM
  • Išleidimo metai: 23-Aug-2010
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9780511922213
  • Formatas: PDF+DRM
  • Išleidimo metai: 23-Aug-2010
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9780511922213

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"Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyze, and use them. CompleteMATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate studentsin engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods"--Provided by publisher.

Provided by publisher.

Recenzijos

' thorough and practical ' Mathematical Reviews

Daugiau informacijos

This text introduces numerical methods and shows how to develop, analyze, and use them.
Preface to the Second Edition ix
Preface to the First Edition xi
1 Interpolation
1(12)
1.1 Lagrange Polynomial Interpolation
1(3)
1.2 Cubic Spline Interpolation
4(4)
Exercises
8(4)
Further Reading
12(1)
2 Numerical Differentiation - Finite Differences
13(17)
2.1 Construction of Difference Formulas Using Taylor Series
13(2)
2.2 A General Technique for Construction of Finite Difference Schemes
15(2)
2.3 An Alternative Measure for the Accuracy of Finite Differences
17(3)
2.4 Pade Approximations
20(3)
2.5 Non-Uniform Grids
23(2)
Exercises
25(4)
Further Reading
29(1)
3 Numerical Integration
30(18)
3.1 Trapezoidal and Simpson's Rules
30(1)
3.2 Error Analysis
31(3)
3.3 Trapezoidal Rule with End-Correction
34(1)
3.4 Romberg Integration and Richardson Extrapolation
35(2)
3.5 Adaptive Quadrature
37(3)
3.6 Gauss Quadrature
40(4)
Exercises
44(3)
Further Reading
47(1)
4 Numerical Solution of Ordinary Differential Equations
48(53)
4.1 Initial Value Problems
48(2)
4.2 Numerical Stability
50(2)
4.3 Stability Analysis for the Euler Method
52(3)
4.4 Implicit or Backward Euler
55(1)
4.5 Numerical Accuracy Revisited
56(2)
4.6 Trapezoidal Method
58(4)
4.7 Linearization for Implicit Methods
62(2)
4.8 Runge-Kutta Methods
64(6)
4.9 Multi-Step Methods
70(4)
4.10 System of First-Order Ordinary Differential Equations
74(4)
4.11 Boundary Value Problems
78(6)
4.11.1 Shooting Method
79(3)
4.11.2 Direct Methods
82(2)
Exercises
84(16)
Further Reading
100(1)
5 Numerical Solution of Partial Differential Equations
101(66)
5.1 Semi-Discretization
102(7)
5.2 von Neumann Stability Analysis
109(2)
5.3 Modified Wavenumber Analysis
111(5)
5.4 Implicit Time Advancement
116(3)
5.5 Accuracy via Modified Equation
119(2)
5.6 Du Fort-Frankel Method: An Inconsistent Scheme
121(3)
5.7 Multi-Dimensions
124(2)
5.8 Implicit Methods in Higher Dimensions
126(2)
5.9 Approximate Factorization
128(9)
5.9.1 Stability of the Factored Scheme
133(1)
5.9.2 Alternating Direction Implicit Methods
134(2)
5.9.3 Mixed and Fractional Step Methods
136(1)
5.10 Elliptic Partial Differential Equations
137(17)
5.10.1 Iterative Solution Methods
140(1)
5.10.2 The Point Jacobi Method
141(2)
5.10.3 Gauss-Seidel Method
143(1)
5.10.4 Successive Over Relaxation Scheme
144(3)
5.10.5 Multigrid Acceleration
147(7)
Exercises
154(12)
Further Reading
166(1)
6 Discrete Transform Methods
167(60)
6.1 Fourier Series
167(9)
6.1.1 Discrete Fourier Series
168(1)
6.1.2 Fast Fourier Transform
169(1)
6.1.3 Fourier Transform of a Real Function
170(2)
6.1.4 Discrete Fourier Series in Higher Dimensions
172(1)
6.1.5 Discrete Fourier Transform of a Product of Two Functions
173(2)
6.1.6 Discrete Sine and Cosine Transforms
175(1)
6.2 Applications of Discrete Fourier Series
176(9)
6.2.1 Direct Solution of Finite Differenced Elliptic Equations
176(4)
6.2.2 Differentiation of a Periodic Function Using Fourier Spectral Method
180(2)
6.2.3 Numerical Solution of Linear, Constant Coefficient Differential Equations with Periodic Boundary Conditions
182(3)
6.3 Matrix Operator for Fourier Spectral Numerical Differentiation
185(3)
6.4 Discrete Chebyshev Transform and Applications
188(12)
6.4.1 Numerical Differentiation Using Chebyshev Polynomials
192(3)
6.4.2 Quadrature Using Chebyshev Polynomials
195(1)
6.4.3 Matrix Form of Chebyshev Collocation Derivative
196(4)
6.5 Method of Weighted Residuals
200(1)
6.6 The Finite Element Method
201(12)
6.6.1 Application of the Finite Element Method to a Boundary Value Problem
202(5)
6.6.2 Comparison with Finite Difference Method
207(2)
6.6.3 Comparison with a Pade Scheme
209(1)
6.6.4 A Time-Dependent Problem
210(3)
6.7 Application to Complex Domains
213(8)
6.7.1 Constructing the Basis Functions
215(6)
Exercises
221(5)
Further Reading
226(1)
A A Review of Linear Algebra
227(8)
A.1 Vectors, Matrices and Elementary Operations
227(3)
A.2 System of Linear Algebraic Equations
230(1)
A.2.1 Effects of Round-off Error
230(1)
A.3 Operations Counts
231(1)
A.4 Eigenvalues and Eigenvectors
232(3)
Index 235
Parviz Moin is the Franklin P. and Caroline M. Johnson Professor of Mechanical Engineering at Stanford University. He received his bachelor's degree in mechanical engineering from the University of Minnesota in 1974 and his master's and PhD degrees in mathematics and mechanical engineering from Stanford in 1978. He held the posts of National Research Council Fellow, Staff Scientist, and Senior Staff Scientist at NASA Ames Research Center. He joined the Stanford faculty in September 1986. He founded the Center for Turbulence Research and the Stanford Institute for Computational and Mathematical Engineering. Currently he is Director of the Center for Turbulence Research and the Department of Energy's Predictive Science Academic Alliance Program at Stanford. He is actively involved in the editorial boards of the Annual Review of Fluid Mechanics, the Journal of Computational Physics, the Physics of Fluids, SIAM Journal of Multi-Scale Modeling and Simulation and the Journal of Flow Turbulence and Combustion. Professor Moin pioneered the use of high fidelity numerical simulations and massively parallel computers for the study of turbulence physics. His distinctions include NASA's Exceptional Scientific Achievement and Outstanding Leadership Medals, the Einstein Professorship of the Chinese Academy of Sciences, the Lawrence Sperry Award of the American Institute of Aeronautics and Astronautics (AIAA), the Fluid Dynamics Prize of the American Physical Society and the Fluid Dynamics Award of AIAA. Professor Moin is a Fellow of the American Physical Society and AIAA. He is a Member of the National Academy of Engineering.