Resolution de quelques problemes en analyse numerique des methodes spectrales
Author: Hervé Vandeven
Publisher:
Published: 1987
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Hervé Vandeven
Publisher:
Published: 1987
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKAuthor: Hervé Vandeven
Publisher:
Published: 1987
Total Pages: 164
ISBN-13:
DOWNLOAD EBOOKANALYSE D'UNE METHODE DE CAPTURE DE CHOC POUR L'APPROXIMATION DES SOLUTIONS D'EQUATIONS HYPERBOLIQUES LINEAIRES PAR DES METHODES SEPCTRALES. METHODE D'AJUSTEMENT AU CHOC POUR L'APPROXIMATION DES SOLUTIONS D'EQUATIONS HYPERBOLIQUES NON LINEAIRES. METHODES SPECTRALES DE TYPE LAGUERRE POUR L'APPROXIMATION DES SOLUTIONS D'UNE EQUATION AUX DERIVEES PARTIELLES DEFINIES DANS UN DOMAINE SEMI-INFINI. APPROXIMATION POLYNOMIALE DES FONCTIONS A DIVERGENCE NULLE. ETUDE DE LA COMPATIBILITE DES ESPACES DISCRETS INTERVENANT DANS L'APPROXIMATION PAR DES METHODES SPECTRALES DES SOLUTIONS DES EQUATIONS DE NAVIER-STOKES
Author: Christine Bernardi
Publisher: Springer
Published: 1992-10-27
Total Pages: 243
ISBN-13: 9783540595762
DOWNLOAD EBOOKLes 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 œuvre. Un formulaire regroupe les formules de base sur les polynômes orthogonaux pour faciliter la lecture. L'ouvrage contient des nombreux exercices.
Author:
Publisher:
Published: 2001
Total Pages: 544
ISBN-13:
DOWNLOAD EBOOKAuthor: Jan S. Hesthaven
Publisher: Cambridge University Press
Published: 2007-01-11
Total Pages: 4
ISBN-13: 113945952X
DOWNLOAD EBOOKSpectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Author: Ben-yu Guo
Publisher: World Scientific
Published: 1998-05-05
Total Pages: 359
ISBN-13: 9814496642
DOWNLOAD EBOOKThis book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
Author: David Gottlieb
Publisher: SIAM
Published: 1977-01-01
Total Pages: 175
ISBN-13: 9781611970425
DOWNLOAD EBOOKA unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Author: Jie Shen
Publisher:
Published: 1987
Total Pages: 156
ISBN-13:
DOWNLOAD EBOOKPRESENTATION DES METHODES SPECTRALES POUR LA RESOLUTION DES EQUATIONS DE STOKES ET DE NAVIER-STOKES. CONSTRUCTION D'UN SCHEMA RESOLVANT RAPIDE DE HELMHOLTZ. APPROXIMATION DU PROBLEME DE STOKES PAR LA METHODE DE TYPE UZAWA ET A L'AIDE DE LA MATRICE D'INFLUENCE. RESULTATS THEORIQUES ET NUMERIQUES. APPROXIMATION DES EQUATIONS DE NAVIER-STOKES D'EVOLUTION A L'AIDE DE SCHEMAS INCONDITIONNELLEMENT STABLES ET CONVERGENTS
Author: Claudio Canuto
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 582
ISBN-13: 3642841082
DOWNLOAD EBOOKThis is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.
Author: ABDOU.. GARBA
Publisher:
Published: 1993
Total Pages: 212
ISBN-13:
DOWNLOAD EBOOKLA PRESENTE ETUDE CONCERNE L'EMPLOI DES METHODES SPECTRALES POUR LA RESOLUTION NUMERIQUE DE PROBLEMES DANS DES GEOMETRIES COMPLEXES. LA PREMIERE PARTIE EST CONSACREE A L'ETUDE DE TECHNIQUES PERMETTANT D'APPLIQUER EFFICACEMENT LES METHODES SPECTRALES DANS DES GEOMETRIES COMPLEXES. LA PREMIERE TECHNIQUE REPOSE SUR UNE TRANSFORMATION DE COORDONNEE POUR SE RAMENER A UN RECTANGLE, LA SECONDE EST CELLE DITE DE PLONGEMENT QUI FAIT APPEL A LA METHODE DE LA MATRICE D'INFLUENCE. LA DEUXIEME PARTIE CONCERNE LE DEVELOPPEMENT D'UNE METHODE NUMERIQUE DE CALCUL DES ECOULEMENTS INSTATIONNAIRES BIDIMENSIONNELS A SURFACE LIBRE D'UN FLUIDE VISQUEUX INCOMPRESSIBLE AVEC PERIODICITE DANS LA DIRECTION HORIZONTALE. LES EQUATIONS SONT CONSIDEREES DANS LA FORMULATION FONCTION DE COURANT-TOURBILLON. UN CHANGEMENT DE VARIABLE BASE SUR LA HAUTEUR DE LA SURFACE LIBRE PERMET D'EFFECTUER LES CALCULS DANS UN DOMAINE FIXE. DEUX TYPES DE SCHEMAS DU SECOND ORDRE EN TEMPS ONT ETE CONSIDERES. LE PREMIER SCHEMA EST SEMI-IMPLICITE ET CONDUIT A UNE RESOLUTION DIRECTE, LE SECOND EST COMPLETEMENT IMPLICITE ET NECESSITE, DE CE FAIT, UNE RESOLUTION ITERATIVE. LA RESOLUTION EN ESPACE, LE TYPE SPECTRAL FOURIER-TCHEBYCHEV, UTILISE LA TECHNIQUE DE MATRICE D'INFLUENCE POUR LA VERIFICATION DES CONDITIONS AUX BORDS ET DE SURFACE LIBRE. CES DEUX SCHEMAS ONT ETE EPROUVES SUR DIVERS EXEMPLES: SOLUTION ANALYTIQUE, AMORTISSEMENT D'UNE VAGUE ET INJECTION-EXTRUSION