  The interaction of plasma with magnetic field in the partially ionised solar
atmosphere is frequently modelled via a single-fluid approximation, which is
valid for the case of a strongly coupled collisional media, such as solar
photosphere and low chromosphere. Under the single-fluid formalism the main
non-ideal effects are described by a series of extra terms in the generalised
induction equation and in the energy conservation equation. These effects are:
Ohmic diffusion, ambipolar diffusion, the Hall effect, and the Biermann battery
effect. From the point of view of the numerical solution of the single-fluid
equations, when ambipolar diffusion or Hall effects dominate can introduce
severe restrictions on the integration time step and can compromise the
stability of the numerical scheme. In this paper we introduce two numerical
schemes to overcome those limitations. The first of them is known as Super
Time-Stepping (STS) and it is designed to overcome the limitations imposed when
the ambipolar diffusion term is dominant. The second scheme is called the Hall
Diffusion Scheme (HDS) and it is used when the Hall term becomes dominant.
These two numerical techniques can be used together by applying Strang operator
splitting. This paper describes the implementation of the STS and HDS schemes
in the single-fluid code Mancha3D. The validation for each of these schemes is
provided by comparing the analytical solution with the numerical one for a
suite of numerical tests.
