Chebyshev and Fourier Spectral Methods

by John P. Boyd

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more. Includes 7 appendices and over 160 text figures.

Genres: Mathematics, Reference

688 pages, Paperback

First published October 18, 1989

About the author

John P. Boyd joined the faculty at the University of Michigan in 1977 and has been professor of atmospheric, oceanic, and space science in the College of Engineering since 1988. Concurrently, he was the founding associate director of the Laboratory for Scientific Computation (now the Michigan Institute for Computational Discovery and Engineering) and as such created the university's M. S. and Ph.D. degrees in scientific computing. His previous books are Chebyshev and Fourier Spectral Methods, 2nd edition,(Dover, 2001) and Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics (Springer, 1998). He has also published 240 journal articles in atmospheric and oceanic dynamics, nonlinear waves, physics, and Chebyshev, Fourier, and RBF spectral methods, as well as 20 science fiction stories.

Reviews

[Kyle · Rating 5 out of 5]

Incredibly clear. This book is great at getting you to understand spectral methods. It uses many examples and Boyd is a master of explaining things in very easy-to-understand ways.

He also has a great voice, and adds some levity to the book with quotations and fun to quote passages. This never detracts, but, in fact, improves the book. I can't resist some quotes to give you a flavor of Boyd's wit, "These three examples should chill the blood of any aspiring computational scientist. Albert Einstein noted “Subtle is the Lord”, which is the great man’s way of saying that your computer program is always trying to kill you. Fear is a very good thing for a numerical analyst. One may wish mournfully for faster silicon, but the only absolutely fatal disease to a scientist is a deficiency of thinking." or "Unfortunately, the resulting system of ODEs in time is a disaster wrapped in a catastrophe: all time-marching schemes for the system are unstable."

You can actually just read through this math book, rather than just jumping around (although it is remarkably self-contained, so that you can jump around). The only "negative" I can think of is that sometimes the proofs are omitted as references to other works, but these are done only when the proof wouldn't add anything enlightening to the situation (so unless you are worried as a mathematician about the specific proof, this may be considered a feature). I'd still prefer to see the proofs, but the references to where the proofs are, are far better than some other books (I'll leave unnamed) where it would simply be omitted or called "trivial."

The bottom line is that this is a wonderful book for learning about Spectral methods, and numerical solving in general. It is full of good examples and explanations and completely worth a read for those interested in spectral methods.