An online tour of spectral methods

Spectral methods are a powerful tool for the high-accuracy numerical solution of ODEs and PDEs in simple domains. Sometimes this technology seems complicated, but it is amazing what can be accomplished in a few inches of Matlab based on the simple idea of a Chebyshev collocation derivative. This talk will be an online tour of the forty short programs from my book recently published by SIAM, "Spectral methods in Matlab". Along the way we will solve, always to many digits of precision, problems including the Laplace, Poisson, biharmonic, wave, Mathieu, Orr-Sommerfeld, Airy, Schrodinger, Helmholtz, KdV, and Allen-Cahn equations. The codes are available on the Web, and the longest is 35 lines long.