## Collocation for finding periodic orbits of ODEs

Every now and again I’m asked how to compute the periodic orbits of ODEs using a boundary value solver. Each time, I go looking for old code that does this and, each time, I can’t find it and end up rewriting the collocation code from scratch. This time I thought I’d put my code here so that I have a better chance of finding it again in the future! The basic idea is to use a Fourier differentiation matrix to approximate the derivatives along the orbit and use a nonlinear solver to ensure that those derivatives match the vector field....