Cargando…
The numerical solution of ordinary and partial differential equations /
The Numerical Solution of Ordinary and Partial Differential Equations.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego, CA :
Academic Press : Harcourt Brace Jovanovich,
�1988.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; The Numerical Solution of Ordinary and Partial Differential Equations; Copyright Page; Table of Contents; Preface; Chapter 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; Chapter 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 Methods1.7 Problems; Chapter 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 Multi-Dimensional Problems; 2.5 A Diffusion-Reaction Example; 2.6 Problems; Chapter 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; Chapter 4. Boundary Value Problems; 4.0 Introduction; 4.1 Finite Difference Methods.
- 4.2 A Nonlinear Example4.3 A Singular Example; 4.4 Shooting Methods; 4.5 Multi-Dimensional Problems; 4.6 Successive Over-Relaxation; 4.7 Successive Over-Relaxation 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; Chapter 5. The Finite Element Method; 5.0 Introduction; 5.1 The Galerkin Method for Boundary Value Problems; 5.2 An Example Using Piecewise Linear Trial Functions; 5.3 An Example Using Cubic Hermite Trial Functions; 5.4 A Singular Example; 5.5 Linear Triangular Elements.
- 5.6 Examples Using Triangular Elements5.7 Time-Dependent Problems; 5.8 A One-Dimensional Example; 5.9 A Time-Dependent Example Using Triangular Elements; 5.10 The Eigenvalue Problem; 5.11 Eigenvalue Examples; 5.12 Problems; Appendix 1: The Fourier Stability Method; Appendix 2: Parallel Algorithms; References; Index.