In the current multi-messenger era of astronomy, the low-inertia limit of magnetohydrodynamics, or “force-free” electrodynamics, has regained attention as a first approximation to the modeling of the anticipated precursor emission from binary neutron star mergers. Over the past two decades, force-free simulations have offered valuable insight into the global properties of isolated neutron star and black hole electrodynamics. However, force-free codes frequently assume a formulation of the equations whose initial value problem is not well-posed for all wave propagation axes, rendering their applicability to more general problems uncertain. In this thesis, I explore the numerical viability of a newly developed formulation of the force-free equations using spectral methods. The new equations enjoy improved mathematical properties while retaining the physical meaning of the original system. In this work, I also complete the formulation by providing a framework suitable for boundary conditions involving neutron stars. Test cases as well as limitations are discussed.