The Instability of the Yee Scheme for the “Magic Time Step”

The fully discrete Yee scheme applied to the dimensionless form of Maxwell's equations in free space is considered. It is shown that the Yee scheme with the `magic time step' is not stable. From the numerical results for the 1D problem, the linear instability for the case of the magic time step is detected when a small perturbation is introduced in such a way as shown in the present paper. It is concluded that the magic time step is not suitable for the Yee scheme since the solution may diverge under a certain small perturbation. (CSA)