  Astrophysical fluids under the influence of magnetic fields are often
subjected to single-fluid or two-fluid approximations. In the case of weakly
ionized plasmas however, this can be inappropriate due to distinct responses
from the multiple constituent species to both collisional and non-collisional
forces. As a result, in dense molecular clouds and proto-stellar accretion
discs for instance, the conductivity of the plasma may be highly anisotropic
leading to phenomena such as Hall and ambipolar diffusion strongly influencing
the dynamics.
  Diffusive processes are known to restrict the stability of conventional
numerical schemes which are not implicit in nature. Furthermore, recent work
establishes that a large Hall term can impose an additional severe stability
limit on standard explicit schemes. Following a previous paper which presented
the one-dimensional case, we describe a fully three-dimensional method which
relaxes the normal restrictions on explicit schemes for multifluid processes.
This is achieved by applying the little known Super TimeStepping technique to
the symmetric (ambipolar) component of the evolution operator for the magnetic
field in the local plasma rest-frame, and the new Hall Diffusion Scheme to the
skew-symmetric (Hall) component.
