  We present a finite-volume, genuinely 4th-order accurate numerical method for
solving the equations of resistive relativistic magnetohydrodynamics (Res-RMHD)
in Cartesian coordinates. In our formulation, the magnetic field is evolved in
time in terms of face-average values via the constrained-transport method while
the remaining variables (density, momentum, energy and electric fields) are
advanced as cell volume-averages. Spatial accuracy employs 5th-order accurate
WENO-Z reconstruction from point values (as described in a companion paper) to
obtain left and right states at zone interfaces. Explicit flux evaluation is
carried out by solving a Riemann problem at cell interfaces, using the
Maxwell-Harten-Lax-van Leer with contact wave resolution (MHLLC). Time stepping
is based on the implicit-explicit (IMEX) Runge-Kutta (RK) methods, of which we
consider both the 3rd-order strong stability preserving SSP3(4,3,3) and a
recent 4th-order additive RK scheme, to cope with the stiffness introduced by
the source term in Ampere's law. Numerical benchmarks are presented in order to
assess the accuracy and robustness of our implementation.
