Numerical analysis of partial differential equations /
"This book provides a comprehensive and self-contained treatment of the numerical methods used to solve partial differential equations (PDEs), as well as both the error and efficiency of the presented methods. Featuring a large selection of theoretical examples and exercises, the book presents...
| Κύριος συγγραφέας: | |
|---|---|
| Μορφή: | Βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Hoboken, N.J. :
Wiley,
[2011]
|
| Σειρά: | Pure and applied mathematics (John Wiley & Sons : Unnumbered)
|
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Preface. Acknowledgments
- Finite Difference.
- Second-Order Approximation for [delta]
- Fourth-Order Approximation for [delta]
- Neumann Boundary Condition
- Polar Coordinates
- Curved Boundary
- Difference Approximation for [delta]
- A Convection-Diffusion Equation
- Appendix: Analysis of Discrete Operators
- Summary and Exercises
- Mathematical Theory of Elliptic PDEs
- Function Spaces
- Derivatives
- Sobolev Spaces
- Sobolev Embedding Theory
- Traces
- Negative Sobolev Spaces
- Some Inequalities and Identities
- Weak Solutions
- Linear Elliptic PDEs
- Appendix: Some Definitions and Theorems
- Summary and Exercises
- Finite Elements. 3.1 Approximate Methods of Solution
- Finite Elements in 1D
- Finite Elements in 2D
- Inverse Estimate
- L2 and Negative-Norm Estimates
- A Posteriori Estimate
- Higher-Order Elements
- Quadrilateral Elements
- Numerical Integration
- Stokes Problem
- Linear Elasticity
- Summary and Exercises
- Numerical Linear Algebra
- Condition Numbers
- Classical Iterative Methods
- Krylov Subspace Methods
- Preconditioning
- Direct Methods
- Appendix: Chebyshev Polynomials
- Summary and Exercises
- Spectral Methods
- Trigonometric Polynomials
- Fourier Spectral Method
- Orthogonal Polynomials
- Spectral Gakerkin and Spectral Tau Methods
- Spectral Collocation
- Polar Coordinates
- Neumann Problems
- Fourth-Order PDEs
- Summary and Exercises
- Evolutionary PDEs
- Finite Difference Schemes for Heat Equation
- Other Time Discretization Schemes
- Convection-Dominated equations
- Finite Element Scheme for Heat Equation
- Spectral Collocation for Heat Equation
- Finite Different Scheme for Wave Equation
- Dispersion
- Summary and Exercises
- Multigrid
- Introduction
- Two-Grid Method
- Practical Multigrid Algorithms
- Finite Element Multigrid
- Summary and Exercises
- Domain Decomposition
- Overlapping Schwarz Methods
- Projections
- Non-overlapping Schwarz Method
- Substructuring Methods
- Optimal Substructuring Methods
- Summary and Exercises
- Infinite Domains
- Absorbing Boundary Conditions
- Dirichlet-Neumann Map
- Perfectly Matched Layer
- Boundary Integral Methods
- Fast Multiple Method
- Summary and Exercises
- Nonlinear Problems
- Newton's Method
- Other Methods
- Some Nonlinear Problems
- Software
- Program Verification
- Summary and Exercises. Answers to Selected Exercises. References. Index.
