  We present an extension to the special relativistic, ideal
magnetohydrodynamics (MHD) equations, designed to capture effects due to
resistivity. The extension takes the simple form of an additional source term
which, when implemented numerically, is shown to emulate the behaviour produced
by a fully resistive MHD description for a range of initial data. The extension
is developed from first principle arguments, and thus requires no fine tuning
of parameters, meaning it can be applied to a wide range of dynamical systems.
Furthermore, our extension does not suffer from the same stiffness issues
arising in resistive MHD, and thus can be evolved quickly using explicit
methods, with performance benefits of roughly an order of magnitude compared to
current methods.
