  When modeling astrophysical fluid flows, it is often appropriate to discard
the canonical magnetohydrodynamic approximation thereby freeing the magnetic
field to diffuse with respect to the bulk velocity field. As a consequence,
however, the induction equation can become problematic to solve via standard
explicit techniques. In particular, the Hall diffusion term admits fast-moving
whistler waves which can impose a vanishing timestep limit.
  Within an explicit differencing framework, a multifluid scheme for weakly
ionised plasmas is presented which relies upon a new approach to integrating
the induction equation efficiently. The first component of this approach is a
relatively unknown method of accelerating the integration of parabolic systems
by enforcing stability over large compound timesteps rather than over each of
the constituent substeps. This method, Super Time Stepping, proves to be very
effective in applying a part of the Hall term up to a known critical value. The
excess of the Hall term above this critical value is then included via a new
scheme for pure Hall diffusion.
