One-step Unconditionally Stable FDTD method and its numerical dispersion analysis

The proposed two-dimensional one-step unconditionally stable finite-difference time-domain algorithm (one-step US-FDTD) is an implicit numerical scheme with second-order accuracy in both time and space. The method is performed using only one procedure, but not two sub-updating procedures. We analytically and numerically verified the algorithm is also unconditionally stable and free of the constraint of the Courant stability condition. The dispersion relation is derived and the dispersion error as algorithm´s time step size and wave propagation angle are investigated. It shows despite the proposed method dispersion error slightly larger than the conventional FDTD, but it is quite simple updating procedure maintaining the same accuracy to the conventional ADI-FDTD.