On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

Abstract

Recently, the stability of the D-E and the J-E auxiliary differential equation (ADE) schemes, which are used in implementing the modified Lorentz dispersive model in the finite difference time domain (FDTD) algorithm, has been studied by Prokopidis and Zografopoulos and it has been concluded that the J-E implementation is proven more restrictive compared to D-E and the D-E implementation is more robust in terms of stability, In order to avoid drawing inaccurate conclusions regarding the J-E ADE-FDTD scheme in general, it is shown in this comment that if the bilinear frequency approximation technique is used in the FDTD discretization of the J-E ADE scheme, one can obtain the same stability polynomial as that of the D-E ADE scheme, and therefore, the same stability conditions will be applied. Hence, the stability limitations of the ADE scheme are based on the FDTD discretization methodology rather than the ADE-method itself. Finally, a numerical example carried out in a one-dimensional domain shows that the presented J-E ADE implementation is numerically stable as well as accurate as the D-E ADE counterpart.