Spectral methods : algorithms, analysis and applications

By: Shen, JieContributor(s): Tang, Tao | Wang, Li-LianSeries: Springer series in computational mathematicsPublication details: Heidelberg: Springer Berlin, [c2011]Description: 470 pISBN: 9783540710400Subject(s): Spectral theory (Mathematics) | Partial differential equationsLOC classification: QC20.7.S64Online resources: Click here to access online
Contents:
1. Introduction 2. Fourier Spectral Methods for Periodic Problems 3. Orthogonal Polynomials and Related Approximation Results 4. Spectral Methods for Second-Order Two-Point Boundary Value Problems 5. Volterra Integral Equations 6. Higher-Order Differential Equations 7. Unbounded Domains 8. Separable Multi-Dimensional Domains 9. Applications in Multi-Dimensional Domains
Summary: 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.---summary provided by publisher
List(s) this item appears in: New Arrivals
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Rack No 9 QC20.7.S64 (Browse shelf (Opens below)) Available 02848
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1. Introduction
2. Fourier Spectral Methods for Periodic Problems
3. Orthogonal Polynomials and Related Approximation Results
4. Spectral Methods for Second-Order Two-Point Boundary Value Problems
5. Volterra Integral Equations
6. Higher-Order Differential Equations
7. Unbounded Domains
8. Separable Multi-Dimensional Domains
9. Applications in Multi-Dimensional Domains

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.---summary provided by publisher

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