Stability of the extended four-step ADI-FDTD method including lumped capacitors

The stability of the four-step alternating direction implicit finite-difference time-domain (ADI-FDTD) method including lumped capacitors is studied. In particular, the implicit different formulation for the lumped capacitor is analyzed. Then, its unconditional stability is analytically proven by the von Neumann method. Finally, its unconditional stability is verified through numerical experiments.