FDTD stability criteria derived in the Z-transform domain

Viewing the FDTD in as a linear system, stability criteria can be applied in a rather straightforward manner. The four dimensional Z-domain is used, where the poles of the temporal transform are sought within the unit circle in the complex plane. This method leads to inequalities that are the same as the one obtained with the traditional Von Neumann analysis. However, in view of the extensive arsenal of stability analyses and stabilization methods in linear system theory, one may anticipate that many of these would be applied to the FDTD in the future.