Cargando…
Numerical methods for partial differential equations /
Numerical Methods for Partial Differential Equations.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1977.
|
| Edición: | 2nd ed. |
| Colección: | Computer science and applied mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Numerical Methods for Partial Differential Equations; Copyright Page; Dedication; Table of Contents; Preface to second edition; Preface to first edition; Chapter 1. Fundamentals; 1-0 Introduction; 1-1 Classification of physical problems; 1-2 Classification of equations; 1-3 Asymptotics; 1-4 Discrete methods; 1-5 Finite differences and computational molecules; 1-6 Finite difference operators; 1 -7 Errors; 1-8 Stability and convergence; 1-9 I rregular boundaries; 1-10 Choice of discrete network; 1-11 Dimensionless forms; REFERENCES; Chapter 2. Parabolic equations; 2-0 Introduction.
- 2-1 Simple explicit methods2-2 Fourier stability method; 2-3 Implicit methods; 2-4 An unconditionally unstable difference equation; 2-5 Matrix stability analysis; 2-6 Extension of matrix stability analysis; 2-7 Consistency, stability, and convergence; 2-8 Pure initial value problems; 2-9 Variable coefficients; 2-10 Examples of equations with variable coefficients; 2-11 General concepts of error reduction; 2-12 Explicit methods for nonlinear problems; 2-13 An application of the explicit method; 2-14 Implicit methods for nonlinear problems; 2-15 Concluding remarks; REFERENCES.
- Chapter 3. Elliptic equations3-0 Introduction; 3-1 Simple finite difference schemes; 3-2 Iterative methods; 3-3 Linear elliptic equations; 3-4 Some point iterative methods; 3-5 Convergence of point iterative methods; 3-6 Rates of convergence; 3-7 Accelerations-successive over-relaxation (SOR); 3-8 Extensions of SOR; 3-9 Qualitative examples of over-relaxation; 3-10 Other point iterative methodsf; 3-11 Block iterative methods; 3-12 Alternating direction methods; 3-13 Summary of ADI results; 3-14 Some nonlinear examples; REFERENCES; Chapter 4. Hyperbolic equations; 4-0 Introduction.
- 4-1 The quasilinear system4-2 Introductory examples; 4-3 Method of characteristics; 4-4 Constant states and simple waves; 4-5 Typical application of characteristics; 4-6 Explicit finite difference methods; 4-7 Overstability; 4-8 Implicit methods for second-order equations; 4-9 Nonlinear examples; 4-10 Simultaneous first-order equations-explicit methods; 4-11 An implicit method for first-order equations; 4-11 An implicit method for first-order equations; 4-13 Gas dynamics in one-space variable; 4-14 Eulerian difference equations; 4-15 Lagrangian difference equations.
- 4-15 Lagrangian difference equations4-16 Hopscotch methods for conservation laws; 4-17 Explicit-implicit schemes for conservation laws; REFERENCES; Chapter 5. Special topics; 5-0 Introduction; 5-1 Singularities; 5-2 Shocks; 5-3 Eigenvalue problems; 5-4 Parabolic equations in several space variables; 5-5 Additional comments on elliptic equations; 5-6 Hyperbolic equations in higher dimensions; 5-7 Mixed systems; 5-8 Higher-order equations in elasticity and vibrations; 5-9 Fluid mechanics: the Navier-Stokes equations; 5-10 Introduction to Monte Carlo methods; 5-11 Method of lines; 5-12 Fast Fourier transform and applications.