Error analysis of an ADI splitting scheme for the inhomogenous Maxwell equations

In this paper we investigate an alternating direction implicit (ADI) time integration scheme for the Maxwell equations with sources, currents and conductivity. We show its stability and efficiency. The main results establish that the scheme converges in a space similar to $H$$^{-1}$ with order two to the solution of the Maxwell system. Moreover, the divergence conditions in the system are preserved in $H$$^{-1}$ with order one.