The FDTD method and its relation to Fibonacci polynomials

In this paper we show that the Finite-Difference Time-Domain method (FDTD method) follows the recurrence relation for Fibonacci polynomials. This observation allows us to easily derive the Courant-Friedrichs-Lewy stability condition by exploiting the connection between Fibonacci polynomials and Chebyshev polynomials of the second kind. In addition, we compare FDTD with the Spectral Lanczos Decomposition method (SLDM) and show that to capture the evolution of the fields in time, SLDM adjust itself to the spectrum of the system matrix, while FDTD takes only extremal eigenvalue information into account.