Lloyd N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000
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