The design of high-order, leap-frog integrators for Maxwell's equations

In this paper, we address issues related to high-order integrator development and propose an extended leap-frog methodology that can achieve temporal accuracy to any even order desired. Such an integrator is compatible with either explicit spatial differencing or with compact differencing; in this paper we consider the former. To limit the discussion, only the fourth-order and eighth-order integrators are presented. The chief attributes of these integrators are that the computational memory requirements are small and the algorithmic complexity is not increased, with respect to the classical FDTD method. To validate many of the theoretical claims made here, numerous studies on the rectangular waveguide are considered. These studies clearly demonstrate the effect of accuracy on data quality.