This is a very lucid introduction to spectral methods emphasizing the mathematical aspects of the theory rather than the many applications in numerical analysis and the engineering sciences. The first part is a fairly complete introduction to Fourier series while the second emphasizes polynomial expansion methods like Chebyshev's. The author gives rigorous proofs of fundamental results related to one-dimensional advection and diffusions equations. The book addresses students as well as practitioners of numerical analysis.

Bibliographic Information

Book Title: An Introduction to the Numerical Analysis of Spectral Methods
Authors: Bertrand Mercier
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/BFb0020591
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1989
Softcover ISBN: 978-3-662-13757-4Published: 23 August 2014
eBook ISBN: 978-3-540-46158-6Published: 13 November 2005
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: V, 154
Number of Illustrations: 1 b/w illustrations
Topics: Mathematical Methods in Physics, Numerical and Computational Physics, Simulation, Fluid- and Aerodynamics, Mathematical and Computational Engineering, Numerical Analysis

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An Introduction to the Numerical Analysis of Spectral Methods

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Table of contents (3 chapters)

Front Matter

Introduction

Fourier spectral method

Polynomial spectral methods

Back Matter

Keywords

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