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๐Ÿ“

Spectral Methods: Algorithms, Analysis and Applications

โœ Scribed by Jie Shen, Tao Tang, Li-Lian Wang (auth.)

Publisher
Springer-Verlag Berlin Heidelberg
Year
2011
Tongue
English
Leaves
487
Series
Springer Series in Computational Mathematics 41
Edition
1
Category
Library
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โœฆ Synopsis

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.

โœฆ Table of Contents

Front Matter....Pages i-xvi
Introduction....Pages 1-22
Fourier Spectral Methods for Periodic Problems....Pages 23-46
Orthogonal Polynomials and Related Approximation Results....Pages 47-140
Spectral Methods for Second-Order Two-Point Boundary Value Problems....Pages 141-180
Volterra Integral Equations....Pages 181-200
Higher-Order Differential Equations....Pages 201-236
Unbounded Domains....Pages 237-298
Separable Multi-Dimensional Domains....Pages 299-366
Applications in Multi-Dimensional Domains....Pages 367-413
Back Matter....Pages 415-470

โœฆ Subjects

Computational Mathematics and Numerical Analysis; Partial Differential Equations; Mathematics of Computing

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