Analysis of the FDTD method via the discrete oscillator

The analysis of the FDTD method is usually performed by assuming an e/sup j/spl omega/t/ time dependence for the field quantities as the response due to a steady-state monochromatic wave excitation. This continuous dependence, when combined with the discrete nature of the Yee grid leads to solution errors and dispersion relations that do not describe accurately the propagation properties in the grid for all frequencies. In this article, the discrete oscillator is introduced and used to study the numerical properties of the FDTD method. Formulas are derived for the propagation characteristics in the one- and two-dimensional cases.