Spectral methods : fundamentals in single domains
 Language
 English.
 Imprint
 Berlin ; New York : Springer, c2006.
 Physical description
 xxii, 563 p. : ill. (some col.) ; 25 cm.
 Series
 Scientific computation.
Access
Available online
 www.springerlink.com SpringerLink
 www.myilibrary.com MyiLibrary
 site.ebrary.com ebrary

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QA377 .S64 2006

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QA377 .S64 2006
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Contributors
 Contributor
 Canuto, C.
Contents/Summary
 Contents

 Introduction. Polynomial Approximation. Basic Approaches to Constructing Spectral Methods. Algebraic Systems and Solution Techniques. Basic Approaches to Constructing Spectral Methods. Algebraic Systems and Solution Techniques. Global Approximation Results. Theory of Stability and Convergence for Spectral Methods. Analysis of Model BoundaryValue Problems. Appendices AE.
 (source: Nielsen Book Data)
 Publisher's Summary
 Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundaryvalue problems. Both the algorithmic and theoretical discussions cover spectral methods on tensorproduct domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms. A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2006
 Responsibility
 C. Canuto ... [et al.].
 Series
 Scientific computation, 14348322
 ISBN
 3540307257
 9783540307259