A modified difference equation with very low numerical dispersion errors

The difference equations arising from a Yee discretization of Maxwell´s equations produce numerical dispersion artifacts whose effects are widely known. Reduction of these effects is important for accurate modelling over a large number of time steps. Conventional methods for tackling this problem include the usage of higher order differencing schemes and denser sampling rates, both approaches resulting in many cases in comparable additional computational burden. In this work, it is suggested to adopt a radically different approach, i.e., construct a family of new difference equations that are not direct discretizations of the continuous equations, but have solutions that are discretized versions of the continuous solutions, and tend to the continuous limit as Deltaz rarr 0 and Deltat rarr 0. The rationale behind these new equations is described. The first formulation involves a narrowband modified difference equation, for which it is shown that a total elimination of numerical dispersion is achieved for a single frequency, with useful results obtained over a certain frequency band. This formulation can be generalized to multiple frequency equations with higher bandwidths