An Introduction to the Numerical Analysis of Spectral Methods (Lecture Notes in Physics 318): Bertrand Mercier

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We hope that this book will serve as an elementary introduction to the mathematical aspects of spectral methods. The first part of the monograph is a reasonably complete introduction to the theory of Fourier series while the second part lays some foundations for the theory of polynomial expansion methods, in particular Chebyshev expansions. No monograph of this size can hope to serve as a comprehensive reference to all aspects of spectral methods. The emphasis here is on proving rigorously some fundamental results related to one-dimensional advection and diffusion equations. No applications of the methods are presented and no revisions have been made to account for results subsequent to 1981. The reader interested in recent theory and applications of spectral methods might wish to consult the book by Canuto et al.




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