Polynomial Approximation of Differential Equations: 8 - Brossura

Funaro, Daniele

Brossura

ISBN 10: 3662138786 ISBN 13: 9783662138786

Casa editrice: Springer, 2014

Riassunto

This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap­ plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be­ ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com­ prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.

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Contenuti

Special Families of Polynomials.- Orthogonality.- Numerical Integration.- Transforms.- Functional Spaces.- Results in Approximation Theory.- Derivative Matrices.- Eigenvalue Analysis.- Ordinary Differential Equations.- Time-Dependent Problems.- Domain-Decomposition Methods.- Examples.- An Example in Two Dimensions.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2014
• ISBN 10: 3662138786
• ISBN 13: 9783662138786
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 320
• Contatto del produttore: {language_tag:it_IT,value:"Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com"}