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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

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Item type	Current library	Shelving location	Call number	Status	Date due	Barcode	Item holds
Book	ICTS	Rack No 9	QC20.7.S64 (Browse shelf (Opens below))	Available		02848

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Previous	QC 20.7.S Interacting particle systems	QC 20.7.S Stochastic processes for physicists	QC20.7.S3 Scattering amplitudes in gauge theory and gravity	QC20.7.S64 Spectral methods : algorithms, analysis and applications	QC20.7.S64 Spectral methods for time-dependent problems	QC20.7.S8 Stochastic processes in physics and chemistry	QC20.7.T65 Topology and Geometry for Physicists	Next

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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