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Spectral Methods [electronic resource] : Algorithms, Analysis and Applications / by Jie Shen, Tao Tang, Li-Lian Wang.

By: Shen, Jie [author.].
Contributor(s): Tang, Tao [author.] | Wang, Li-Lian [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Series in Computational Mathematics: 41Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Description: XVI, 472 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540710417.Subject(s): Mathematics | Computer science | Differential equations, partial | Computer science -- Mathematics | Mathematics | Computational Mathematics and Numerical Analysis | Partial Differential Equations | Mathematics of ComputingDDC classification: 518 | 518 Online resources: Click here to access online
Contents:
Introduction -- Fourier Spectral Methods for Periodic Problems -- Orthogonol Polynomials and Related Approximation Results -- Second-Order Two-Point Boundary Value Problems -- Integral Equations -- High-Order Differential Equations -- Problems in Unbounded Domains -- Multi-Dimensional Domains -- Mathematical Preliminaries -- Basic iterative methods -- Basic time discretization schemes -- Instructions for routines in Matlab.  .
In: Springer eBooksSummary: Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of  basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
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Introduction -- Fourier Spectral Methods for Periodic Problems -- Orthogonol Polynomials and Related Approximation Results -- Second-Order Two-Point Boundary Value Problems -- Integral Equations -- High-Order Differential Equations -- Problems in Unbounded Domains -- Multi-Dimensional Domains -- Mathematical Preliminaries -- Basic iterative methods -- Basic time discretization schemes -- Instructions for routines in Matlab.  .

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of  basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

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