### SPECTRAL METHODS IN MATLAB Lloyd N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000

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This 160-page book is built around forty short Matlab programs, or "M-files", which do everything from demonstrating spectral accuracy on functions of varying smoothness to solving the Poisson, biharmonic, Orr-Sommerfeld, KdV, and Allen-Cahn equations.

A glaring omission in the book is that it does not treat barycentric interpolation (apart from a few exercises); this is a simple, powerful tool that anyone using spectral methods should be aware of. See the papers by Berrut and T. and also Chebfun, a spectral-style system for dealing with functions in object-oriented MATLAB.

Sample chapters:
Front matter, Chapter 1, Chapter 6, Chapter 9
Same material in pdf format

M-files:
cheb.m, chebfft.m, gauss.m, clencurt.m
p1.m, p2.m, p3.m, p4.m, p5.m, p6.m, p6u.m, p7.m, p8.m, p9.m, p10.m, p11.m, p12.m, p13.m, p14.m, p15.m, p16.m, p17.m, p18.m, p19.m, p20.m, p20u.m, p21.m, p22.m, p23.m, p23a.m, p24.m, p24fine.m, p25.m, p26.m, p27.m, p28.m, p28b.m, p29.m, p30.m, p30b.m, p30c.m, p31.m, p32.m, p33.m, p34.m, p35.m, p36.m, p37.m, p38.m, p39.m, p40.m
All the M-files (text)
All the M-files (zip archive)
All the M_files (gzipped tar archive)

Nick Trefethen
Oxford University Mathematical Institute
Oxford OX2 6GG
United Kingdom
trefethen@maths.ox.ac.uk