| Titre : |
A first course in the numerical analysis of differential equations |
| Type de document : |
texte imprimé |
| Auteurs : |
Arieh ISERLES, Auteur |
| Editeur : |
Cambridge university press |
| Année de publication : |
2000 |
| Importance : |
378 p. |
| Format : |
25 cm. |
| ISBN/ISSN/EAN : |
978-0-521-55655-2 |
| Note générale : |
Index. |
| Langues : |
Anglais (eng) |
| Catégories : |
MATHÉMATIQUES:Analyse
|
| Index. décimale : |
04-02 Analyse |
| Résumé : |
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
Table des matières
ORDINARY DIFFERENTIAL EQUATIONS
Euler's method and beyond
Multistep methods
RungeKutta methods
Stiff equations
Error control
Nonlinear algebraic systems
THE POISSON EQUATION
Finite difference schemes
The finite element method
Gaussian elimination for sparse linear equations
Iterative methods for sparse linear equations
Multigrid techniques
Fast Poisson solvers
PARTIAL DIFFERENTIAL EQUATIONS OF EVOLUTION
The diffusion equation
Hyperbolic equations
Appendix Bluffers guide to useful mathematics
Index |
A first course in the numerical analysis of differential equations [texte imprimé] / Arieh ISERLES, Auteur . - Cambridge university press, 2000 . - 378 p. ; 25 cm. ISBN : 978-0-521-55655-2 Index. Langues : Anglais ( eng)
| Catégories : |
MATHÉMATIQUES:Analyse
|
| Index. décimale : |
04-02 Analyse |
| Résumé : |
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
Table des matières
ORDINARY DIFFERENTIAL EQUATIONS
Euler's method and beyond
Multistep methods
RungeKutta methods
Stiff equations
Error control
Nonlinear algebraic systems
THE POISSON EQUATION
Finite difference schemes
The finite element method
Gaussian elimination for sparse linear equations
Iterative methods for sparse linear equations
Multigrid techniques
Fast Poisson solvers
PARTIAL DIFFERENTIAL EQUATIONS OF EVOLUTION
The diffusion equation
Hyperbolic equations
Appendix Bluffers guide to useful mathematics
Index |
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