Unification of leapfrog and crank⇓Nicolson finite difference time domain methods

In this paper we present a unified theory of explicit (leapfrog) and implicit (Crank–Nicolson) finite difference time domain (FDTD) time-stepping schemes. This enables us to interface leapfrog FDTD with Crank–Nicolson FDTD and we will prove that the result is stable at the Courant limit of the leapfrog part. It also enables us to construct explicit FDTD-like algorithms whose stability condition is less restrictive than that of leapfrog FDTD, and a remarkable explicit 1:2 FDTD refinement scheme which is stable up to the Courant limit of the coarse part.