  Partially ionized plasmas, such as the solar chromosphere, require a
generalized Ohm's law including the effects of ambipolar and Hall drift. While
both describe transport processes that arise from the multifluid equations and
are therefore of hyperbolic nature, they are often incorporated in models as a
diffusive, i.e. parabolic process. While the formulation as such is easy to
include in standard MHD models, the resulting diffusive time-step constraints
do require often a computationally more expensive implicit treatment or
super-time-stepping approaches. In this paper we discuss an implementation that
retains the hyperbolic nature and allows for an explicit integration with small
computational overhead. In the case of ambipolar drift, this formulation arises
naturally by simply retaining a time derivative of the drift velocity that is
typically omitted. This alone leads to time-step constraints that are
comparable to the native MHD time-step constraint for a solar setup including
the region from photosphere to lower solar corona. We discuss an accelerated
treatment that can further reduce time-step constraints if necessary. In the
case of Hall drift we propose a hyperbolic formulation that is numerically
similar to that for the ambipolar drift and we show that the combination of
both can be applied to simulations of the solar chromosphere at minimal
computational expense.
