On the Stability of the RK-FDTD Method for Graphene Modeling - Pereda, Jose A.; Grande, Ana (IEEE transactions on antennas and propagation, 2025)
The Runge-Kutta finite-difference time-domain (RK-FDTD) method is an extension of the conventional FDTD technique to include graphene sheets. According to this method, the relationship between the current density and the electric field for graphene is discretized by applying an explicit second-order RK scheme. It has recently been concluded that the RK-FDTD method is subject to the same Courant-Friedrichs-Lewy (CFL) stability limit as the conventional FDTD method. This communication revisits the stability analysis of the RK-FDTD method. To this end, the von Neumann method is combined with the Routh-Hurwitz criterion. As a result, closed-form stability conditions are obtained. It is shown that in addition to the CFL stability limit, the RK-FDTD method must also satisfy new conditions involving graphene parameters. Unfortunately, the RK-FDTD method becomes unstable for commonly used values of these parameters. The theoretical results are confirmed with numerical examples.