  Many astrophysical processes involving magnetic fields and quasi-stationary
processes are well described when assuming the fluid as a perfect conductor.
For these systems, the ideal-magnetohydrodynamics (MHD) description captures
the dynamics effectively and a number of well-tested techniques exist for its
numerical solution. Yet, there are several astrophysical processes involving
magnetic fields which are highly dynamical and for which resistive effects can
play an important role. The numerical modeling of such non-ideal MHD flows is
significantly more challenging as the resistivity is expected to change of
several orders of magnitude across the flow and the equations are then either
of hyperbolic-parabolic nature or hyperbolic with stiff terms. We here present
a novel approach for the solution of these relativistic resistive MHD equations
exploiting the properties of implicit-explicit (IMEX) Runge Kutta methods. By
examining a number of tests we illustrate the accuracy of our approach under a
variety of conditions and highlight its robustness when compared with
alternative methods, such as the Strang-splitting. Most importantly, we show
that our approach allows one to treat, within a unified framework, both those
regions of the flow which are fluid-pressure dominated (such as in the interior
of compact objects) and those which are instead magnetic-pressure dominated
(such as in their magnetospheres)
