  This paper describes a numerical scheme for multi-fluid hydrodynamics in the
limit of small mass densities of the charged particles. The inertia of the
charged particles can then be neglected, which makes it possible to write an
evolution equation for the magnetic field that can be solved using an implicit
scheme. This avoids the severe restriction on the stable timestep that would
otherwise arise at high resolution, or when the Hall effect is large. Numerical
tests show that the scheme can accurately model steady multi-fluid shock
structures both with and without sub-shocks. Although the emphasis is on shocks
in molecular clouds, a multi-dimensional version of this code could be applied
to any Astrophysical flow in which ambi-polar diffusion or the Hall effect, or
both play a significant role.
