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Approximations Spectrales de Problèmes Aux Limites Elliptiques
Paperback
Series: Mathématiques Et Applications, Book 10
ISBN13: 9783540595762
Publisher: Springer
Published: Oct 27 1992
Pages: 243
Weight: 0.78
Height: 0.52 Width: 6.14 Depth: 9.21
Language: French
Les méthodes spectrales sont une technique récente d'approximation de la solution d'équations aux dérivées partielles par des polynômes de haut degré. Elles ont un degré de précision infini: l'ordre de l'erreur ne dépend que de la solution à approcher. Leur utilisation s'est énormément développée ces dernières années.
Le sujet de ce livre est l'analyse numérique des méthodes spectrales. Il présente de façon unifiée les notions de base, parmi lesquelles certains résultats récents, et donne quelques applications (en particulier la discrétisation du problème de Stokes). Une attention particulière est portée à l'optimalité des résultats, démontrée grâce à des contre-exemples appropriés. La lecture du livre permet aux étudiants de D.E.A. d'analyse numérique et aux chercheurs intéressés par le sujet d'acquérir une connaissance complète de la méthode pour des problèmes modèle, ainsi que les idées de base permettant de la mettre en oeuvre.
Un formulaire regroupe les formules de base sur les polynômes orthogonaux pour faciliter la lecture. L'ouvrage contient des nombreux exercices.
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