Analyzing the stability of the FDTD technique by combining the von Neumannmethod with the Routh-Hurnitz criterion

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the von Neumann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expre ssions. This technique is applied to the problem of determining the stabili ty conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispers ive media are considered. It is shown that, for the former case, the stabil ity limit of the conventional FDTD method is preserved. However, for the la tter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of t he conventional FDTD method to be maintained.