Fundamentals of Engineering Numerical Analysis

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Cambridge University Press, 20/08/2001 - 209 páginas
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Engineers need hands-on experience in solving complex engineering problems with computers. This text introduces numerical methods and shows how to develop, analyze, and use them. A thorough and practical book, it is is intended as a first course in numerical analysis, primarily for beginning graduate students in 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. They will learn what factors affect accuracy, stability, and convergence. A special feature is the numerous examples and exercises that are included to give students first-hand experience.
 

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Índice

INTERPOLATION
1
12 Cubic Spline Interpolation
4
Exercises
8
Further Reading
11
NUMERICAL DIFFERENTIATION FINITE DIFFERENCES
12
22 A General Technique for Construction of Finite Difference Schemes
14
23 An Alternative Measure for the Accuracy of Finite Differences
16
24 Pade Approximations
19
55 Accuracy via Modified Equation
111
An Inconsistent Scheme
113
57 MultiDimensions
116
58 Implicit Methods in Higher Dimensions
118
59 Approximate Factorization
120
591 Stability of the Factored Scheme
125
592 Alternating Direction Implicit Methods
126
593 Mixed and Fractional Step Methods
128

25 NonUniform Grids
22
Exercises
24
Further Reading
26
NUMERICAL INTEGRATION
27
32 Error Analysis
28
33 Trapezoidal Rule with EndCorrection
31
34 Romberg Integration and Richardson Extrapolation
32
35 Adaptive Quadrature
34
36 Gauss Quadrature
37
Exercises
41
Further Reading
42
NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
43
42 Numerical Stability
45
43 Stability Analysis for the Euler Method
47
44 Implicit or Backward Euler
50
45 Numerical Accuracy Revisited
51
46 Trapezoidal Method
53
47 Linearization for Implicit Methods
57
48 RungeKutta Methods
59
49 MultiStep Methods
65
410 System of FirstOrder Ordinary Differential Equations
69
411 Boundary Value Problems
73
4111 Shooting Method
74
4112 Direct Methods
77
Exercises
79
Further Reading
92
NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
93
51 SemiDiscretization
94
52 von Neumann Stability Analysis
101
53 Modified Wavenumber Analysis
103
54 Implicit Time Advancement
108
510 Elliptic Partial Differential Equations
129
5101 Iterative Solution Methods
132
5102 The Point Jacobi Method
133
5103 GaussSeidel Method
135
5104 Successive Over Relaxation Scheme
136
5105 Multigrid Acceleration
139
Exercises
146
Further Reading
156
DISCRETE TRANSFORM METHODS
157
611 Discrete Fourier Series
158
612 Fast Fourier Transform
159
613 Fourier Transform of a Real Function
160
614 Discrete Fourier Series in Higher Dimensions
162
615 Discrete Fourier Transform of a Product of Two Functions
163
616 Discrete Sine and Cosine Transforms
164
62 Applications of Discrete Fourier Series
166
622 Differentiation of a Periodic Function Using Fourier Spectral Method
170
623 Numerical Solution of Linear Constant Coefficient Differential Equations with Periodic Boundary Conditions
172
63 Matrix Operator for Fourier Spectral Numerical Differentiation
175
64 Discrete Chebyshev Transform and Applications
178
641 Numerical Differentiation Using Chebyshev Polynomials
182
642 Quadrature Using Chebyshev Polynomials
185
643 Matrix Form of Chebyshev Collocation Derivative
186
Exercises
190
Further Reading
194
A REVIEW OF LINEAR ALGEBRA
195
A2 System of Linear Algebraic Equations
198
A3 Operations Counts
199
A4 Eigenvalues and Eigenvectors
200
Index
203
Direitos de autor

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Fundamentals of Engineering Numerical Analysis
Parviz Moin
Pré-visualização limitada - 2001
Fundamentals of Engineering Numerical Analysis
Parviz Moin
Pré-visualização indisponível - 2001

Palavras e frases frequentes

accuracy accurate advancement algorithm analysis application approximation boundary conditions calculate called Chapter Chebyshev complex Consider convergence corresponding data points defined derivative diagonal difference scheme differential equations direction discrete discuss domain eigenvalues elements error evaluations exact solution example Exercise expansion explicit Euler expression factor Figure finite difference Fourier Fourier coefficients Fourier transform fourth-order function given gives grid points heat equation higher initial integral interpolation interval iterations leads linear matrix maximum mesh modified wavenumber non-linear Note numerical methods numerical solution obtained ODEs operator partial differential equations periodic physical Plot polynomial problem programs properties quadrature reduce residual right-hand side rule Runge–Kutta scheme shown simply solve space spatial spline stability step Substituting Taylor series technique tion transform trapezoidal tridiagonal vector written zero

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QR code for Fundamentals of Engineering Numerical Analysis
TítuloFundamentals of Engineering Numerical Analysis
Fundamentals of Engineering Numerical Analysis, Parviz Moin
AutorParviz Moin
Ediçãoilustrada, reimpressão
EditoraCambridge University Press, 2001
ISBN0521805260, 9780521805261
Número de páginas209 páginas
  
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