Finite difference time domain dispersion reduction schemes

The finite-difference-time-domain (FDTD), although recognized as a flexible, robust and simple to implement method for solving complex electromagnetic problems, is subject to numerical dispersion errors. In addition to the traditional ways for reducing dispersion, i.e., increasing sampling rate and using higher order degrees of accuracy, a number of schemes have been proposed recently. In this work, an unified methodology for deriving new difference schemes is presented. It is based on certain modifications of the characteristic equation that accompanies any given discretized version of the wave equation. The method is duly compared with existing schemes and verified numerically.