The Chebfun Examples have been written by various authors beginning in 2010. New Examples are always welcome!—download ExampleTemplate.m to get started, and if you have a draft, get in touch.
The Examples are updated from time to time, but the original date is retained. That is why, for example, you will sometimes see an example dated in one year referencing a paper from a later year.

Timedependent PDEs on a periodic interval with
expm
Hadrien Montanelli, December 2014

Pythagorean planets
Behnam Hashemi and Nick Trefethen, December 2014

Periodic ODE eigenvalue problems
Hadrien Montanelli, December 2014

Nonlinear Periodic ODE
Hadrien Montanelli, December 2014

Gallery and Gallerytrig
Hrothgar and Nick Trefethen, December 2014

Fourier Spectral Collocation
Hadrien Montanelli, December 2014

A periodic ODE system
Nick Hale, December 2014