  The main objective of this paper is to develop a general method of geometric
discretization for infinite-dimensional systems and apply this method to the
EPDiff equation. The method described below extends one developed by Pavlov et
al. for incompressible Euler fluids. Here this method is presented in a general
case applicable to all, not only divergence-free, vector fields. Also, a
different (pseudospectral) representation of the velocity field is used. We
will apply this method to the one-dimensional EPDiff equation and present
numerical results.
