An analytical solution to Yee´s FDTD partial difference equations for a one-dimensional cavity problem via z-transform

Yee´s FDTD method has been very popular for computational electromagnetics. However, few authors attempted to solve the partial difference equations in Yee´s method analytically. To the author´s knowledge, only a frequency domain solution for propagation in homogeneous isotropic media (the so-called numerical dispersion relation) was given before. This paper proposes a new analytical solution to Yee´s FDTD partial difference equations for a ID cavity problem via z-transform. This solution enables us to identify differences of the Yee scheme from the exact continuous wave solution easily.