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.