University of Washington
Prof. Nathan Kutz,
an expert in nolinear wave equations, teaches a course on  scientific computing (see its notes here).

Northwestern University
Prof. Hermann Riecke,
an expert in the reaction-diffusion equations, computational neuroscience and such, teaches several courses on numerical methods. Among them is a course on spectral methods for PDEs, and a few others. Check out this useful and impressive website!

Royal Institute of Technology (Sweden)
A concise on-line course on numerical PDEs, including hyperbolic ones, with some examples of codes.
by Prof. Andre Jaun.