A comprehensive new methodology for formulating FDTD schemes with controlled order of accuracy and dispersion

Numerical dispersion errors in the finite-difference-time-domain (FDTD) method have been treated by higher order schemes, coefficient modification schemes, and dispersion relation preserving and non-standard schemes. In this work, a unified methodology for the above methods is formulated, based on the spatial-temporal (k - omega) spectral domain representation of the wave equation (direct application to the Maxwell's equation is also feasible). New difference schemes, adapted to the characteristics of the excitation, can now be derived.