A simple demonstration of numerical dispersion under FDTD [for EM field calculations]

The method of finite differences in the time domain (FDTD) has become of growing importance for solving electromagnetic problems due to its simplicity, versatility and the availabilty of inexpensive and powerful computers. In this work we try to demonstrate in an understandable way the characteristic of numerical dispersion of the algorithm. For this purpose we simulate the one-dimensional propagation of different wave shapes under FDTD. In order to enhance the fact that the dispersion arises as a consequence of the different phase and group velocities for monochromatic waves, we decompose the signals into spectral components and, after propagation at the phase speed given by FDTD, we reconstruct the signals. This computation gives the same results as FDTD. Finally, we compute the propagation, assuming that the phase speed its truly the speed in vacuum. In this case no dispersion its observed at all.