@article{10902/38364,
year = {2025},
month = {10},
url = {https://hdl.handle.net/10902/38364},
abstract = {The Runge Kutta finite-difference time-domain (RK-FDTD) method is an extension of the conventional finite-difference time-domain (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 Runge-Kutta (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 (RH) 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.},
organization = {This work was supported by the Spanish Ministerio de Ciencia e Innovación under Grant PID2022-137619NB-I00.},
publisher = {Institute of Electrical and Electronics Engineers Inc.},
publisher = {IEEE Transactions on Antennas and Propagation, 2025, 73(10), 8238-8241},
title = {On the stability of the RK-FDTD method for graphene modeling},
author = {Pereda Fernández, José Antonio and Grande Sáez, Ana María},
}