The numerical solution of ordinary and partial differential equations /
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| Author / Creator: | Sewell, Granville. |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | Hoboken, N.J. : John Wiley, 2005. |
| Description: | xii, 333 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Pure and applied mathematics; a Wiley-Interscience series of texts, monographs, and tracts Pure and applied mathematics (John Wiley & Sons : Unnumbered) |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5929952 |
Table of Contents:
- Preface
- 0. Direct Solution of Linear Systems
- 0.0. Introduction
- 0.1. General Linear Systems
- 0.2. Systems Requiring No Pivoting
- 0.3. The LU Decomposition
- 0.4. Banded Linear Systems
- 0.5. Sparse Direct Methods
- 0.6. Problems
- 1. Initial Value Ordinary Differential Equations
- 1.0. Introduction
- 1.1. Euler's Method
- 1.2. Truncation Error, Stability, and Convergence
- 1.3. Multistep Methods
- 1.4. Adams Multistep Methods
- 1.5. Backward Difference Methods for Stiff Problems
- 1.6. Runge-Kutta Methods
- 1.7. Problems
- 2. The Initial Value Diffusion Problem
- 2.0. Introduction
- 2.1. An Explicit Method
- 2.2. Implicit Methods
- 2.3. A One-Dimensional Example
- 2.4. Multidimensional Problems
- 2.5. A Diffusion-Reaction Example
- 2.6. Problems
- 3. The Initial Value Transport and Wave Problems
- 3.0. Introduction
- 3.1. Explicit Methods for the Transport Problem
- 3.2. The Method of Characteristics
- 3.3. An Explicit Method for the Wave Equation
- 3.4. A Damped Wave Example
- 3.5. Problems
- 4. Boundary Value Problems
- 4.0. Introduction
- 4.1. Finite Difference Methods
- 4.2. A Nonlinear Example
- 4.3. A Singular Example
- 4.4. Shooting Methods
- 4.5. Multidimensional Problems
- 4.6. Successive Overrelaxation
- 4.7. Successive Overrelaxation Examples
- 4.8. The Conjugate-Gradient Method
- 4.9. Systems of Differential Equations
- 4.10. The Eigenvalue Problem
- 4.11. The Inverse Power Method
- 4.12. Problems
- 5. The Finite Element Method
- 5.0. Introduction
- 5.1. The Galerkin Method
- 5.2. Example Using Piecewise Linear Trial Functions
- 5.3. Example Using Cubic Hermite Trial Functions
- 5.4. A Singular Example and The Collocation Method
- 5.5. Linear Triangular Elements
- 5.6. An Example Using Triangular Elements
- 5.7. Time-Dependent Problems
- 5.8. A One-Dimensional Example
- 5.9. Time-Dependent Example Using Triangles
- 5.10. The Eigenvalue Problem
- 5.11. Eigenvalue Examples
- 5.12. Problems
- Appendix A. Solving PDEs with PDE2D
- A.1. History
- A.2. The PDE2D Interactive User Interface
- A.3. One-Dimensional Steady-State Problems
- A.4. Two-Dimensional Steady-State Problems
- A.5. Three-Dimensional Steady-State Problems
- A.6. Nonrectangular 3D Regions
- A.7. Time-Dependent Problems
- A.8. Eigenvalue Problems
- A.9. The PDE2D Parallel Linear System Solvers
- A.10. Examples
- A.11. Problems
- Appendix B. The Fourier Stability Method
- Appendix C. MATLAB Programs
- Appendix D. Can "ANYTHING" Happen in an Open System?
- Appendix E. Answers to Selected Exercises
- References
