文档介绍：Chebyshev and Fourier Spectral Methods
Second Edition
John P. Boyd
University of Michigan
Ann Arbor, Michigan 48109-2143
email: ******@
./
jpboyd/
2000
DOVER Publications, Inc.
31 East 2nd Street
Mineola, New York 11501
1
Dedication
To Marilyn, Ian, and Emma
“putation is a temptation that should be resisted as
long as possible.”
— J. P. Boyd, paraphrasing T. S. Eliot
i
Contents
PREFACE x
Acknowledgments xiv
Errata and Extended-Bibliography xvi
1 Introduction 1
Series expansions .................................. 1
First Example .................................... 2
with finite element methods .................... 4
with Finite Differences ....................... 6
puters ................................. 9
Choice of basis functions .............................. 9
Boundary conditions ................................ 10
Non-Interpolating and Pseudospectral ...................... 12
Nonlinearity ..................................... 13
Time-dependent problems ............................. 15
FAQ: Frequently Asked Questions ........................ 16
The Chrysalis .................................... 17
2 Chebyshev & Fourier Series 19
Introduction ..................................... 19
Fourier series .................................... 20
Orders of Convergence ............................... 25
Convergence Order ................................. 27
Assumption of Equal Errors ............................ 31
Darboux’s Principle ................................. 32
Why Taylor Series Fail ............................... 35
Location of Singularities .............................. 36
Corner Singularities & Compatibility Conditions ........... 37
FACE: Integration-by-Parts Bound ........................ 41
Asymptotic Calculation of Fourier Coefficients .....