  In this work we present a proof of concept of CUDA-capable, resistive,
multi-fluid models of relativistic magnetohydrodynamics (RMHD). Resistive and
multi-fluid codes for simulating models of RMHD suffer from stiff source terms,
so it is common to implement a set of semi-implicit time integrators to
maintain numerical stability. We show, for the first time, that finite volume
IMEX schemes for resistive and two-fluid models of RMHD can be accelerated by
execution on graphics processing units, significantly reducing the demand set
by these kinds of problems. We report parallel speed-ups of over 21$\times$
using double precision floating-point accuracy, and highlight the optimisation
strategies required for these schemes, and how they differ from ideal RMHD
models. The impact of these results is discussed in the context of the
next-generation simulations of neutron star mergers.
