The instability of the Yee scheme for the ``magic time step'' (Q5929929)

From the text: We show that the Yee scheme is not stable when \(\Delta t = \Delta x\) for the one-dimensional case and \(\Delta t = 1/ \sqrt{(1/ \Delta x)^2 + (1/\Delta y)^2}\) for the two-dimensional case. ThisNEWLINEmeans that one cannot take the maximum \(t\) referred to as the ``magic time step''.NEWLINENEWLINEWe consider the fully discrete Yee scheme applied to the dimensionless form of Maxwell's equations in free space. Fourier transformation of the scheme gives us a linear system with an amplification matrix \(Q\). In order to analyze the stability of the scheme, we investigate the properties of the amplification matrix.