  The time evolution of several interacting Ginzburg-Landau vortices according
to an equation of Schroedinger type is approximated by motion on a
finite-dimensional manifold. That manifold is defined as an unstable manifold
of an auxiliary dynamical system, namely the gradient flow of the
Ginzburg-Landau energy functional. For two vortices the relevant unstable
manifold is constructed numerically and the induced dynamics is computed. The
resulting model provides a complete picture of the vortex motion for arbitrary
vortex separation, including well-separated and nearly coincident vortices.
