On the stability of the finite-difference time-domain method (Q1587873)

The finite difference time domain method used for solving transient electromagnetic fields is studied. Maxwell equations are introduced, normalized and written in terms of an iteration matrix form. The eigenvalue problem for this matrix is analysed. From this analysis a necessary and sufficient conditon for the finite-difference time domain method is found. It is also shown that for a particular step the 2-norm of the finite-difference time domain iteration matrix is equal to the golden ratio. The application of the stability condition in practice is shown. The results are illustrated for a simple one-dimensional configuration.