000			03153 a2200289 4500
003			OSt
005			20240909160555.0
008			240909b |||||||| |||| 00| 0 eng d
020			_a9783540307259
040			_aICTS-TIFR
050			_aQA320 .S626
100			_aCanuto, Claudio
245			_aSpectral methods : fundamentals in single domains
260			_bSpringer Berlin, _aHeidelberg: _c[c2006]
300			_a563 p.
490			_aScientific computation
505			_a1. Introduction 2. Polynomial Approximation 3. Basic Approaches to Constructing Spectral Methods 4. Algebraic Systems and Solution Techniques 5. Polynomial Approximation Theory 6. Theory of Stability and Convergence 7. Analysis of Model Boundary-Value Problems
520			_aSince 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 boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product 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.---summary provided by publisher
650			_aPartial differential equations > Numerical solutions.
650			_aNumerical analysis
650			_aSpectral theory (Mathematics)
700			_aHussaini, M. Youssuff
700			_aQuarteroni, Alfio
700			_aZang, Thomas A.
856			_uhttps://doi.org/10.1007/978-3-540-30726-6
942			_2lcc _cBK
999			_c35122 _d35122