The title of my M.Sc. Dissertation is:

Spectral Methods on a Massively Parallel Computer.

The purpose was to compute solutions to a number of partial differential equations.

The PDE's were transformed to ordinary differential equations by use of Fourier transformations,
the ODE's were then discretized and integrated in time on a massively
parallel computer, a TMC CM-200.

Click in the picture to see an animation of such a solution to the Hasegawa-Mima equation

Here is the dissertation (4.43MB gzip'ed PostScript).