Differential equations and solution of ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Differential equations and solution of linear systems
Auteur(s) :
Laminie, Jacques [Auteur]
Laboratoire de Mathématiques Informatique et Applications [LAMIA]
Chehab, Jean-Paul [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire de Mathématiques Informatique et Applications [LAMIA]
Chehab, Jean-Paul [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Titre de la revue :
Numerical Algorithms
Pagination :
103-124
Éditeur :
Springer Verlag
Date de publication :
2005
ISSN :
1017-1398
Mot(s)-clé(s) en anglais :
Differential equation
Numerical schemes
Numerical linear algebra
Preconditioning
Numerical schemes
Numerical linear algebra
Preconditioning
Discipline(s) HAL :
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical ...
Lire la suite >Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical methods in numerical linear algebra by modelling the linear system to be solved as a given state of a dynamical system; the solution can be reached asymptotically, as a (asymptotically stable) steady state, but also as a finite time (shooting methods). In that way, any (stable) numerical scheme for the integration of such a problem can be presented as a method for solving linear systems. The authors discuss aspects of this approach, which allows them to recover some known methods but also to introduce new ones. Finally, some convergence results and numerical illustrations are presented.Lire moins >
Lire la suite >Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretisation of differential systems. In this article the authors propose generating numerical methods in numerical linear algebra by modelling the linear system to be solved as a given state of a dynamical system; the solution can be reached asymptotically, as a (asymptotically stable) steady state, but also as a finite time (shooting methods). In that way, any (stable) numerical scheme for the integration of such a problem can be presented as a method for solving linear systems. The authors discuss aspects of this approach, which allows them to recover some known methods but also to introduce new ones. Finally, some convergence results and numerical illustrations are presented.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
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