  We describe a novel operator-splitting approach to numerical relativistic
magnetohydrodynamics designed to expand its applicability to the domain of
ultra-high magnetisation. In this approach, the electromagnetic field is split
into the force-free component, governed by the equations of force-free
degenerate electrodynamics (FFDE), and the perturbation component, governed by
the perturbation equations derived from the full system of relativistic
magnetohydrodynamics (RMHD). The combined system of the FFDE and perturbation
equations is integrated simultaneously, for which various numerical techniques
developed for hyperbolic conservation laws can be used. At the end of every
time-step of numerical integration, the force-free and the perturbation
components of the electromagnetic field are recombined and the result is
regarded as the initial value of the force-free component for the next
time-step, whereas the initial value of the perturbation component is set to
zero. To explore the potential of this approach, we build a 3rd-order WENO
code, which was used to carry out 1D and 2D test simulations. Their results
show that this operator-splitting approach allows us to bypass the stiffness of
RMHD in the ultra-high-magnetisation regime where the perturbation component
becomes very small. At the same time, the cod
