Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations

Abstract

The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, “Stability and phase error analysis of FD-TD in dispersive dielectrics”, IEEE Transactions on Antennas and Propagation, vol. 42, no. 1, pp. 62–69, 1994), where numerical evidence for specific media have been used. We use von Neumann analysis to give necessary and sufficient stability conditions for these schemes for any medium, in accordance with the partial results of [1].