On the stability of the finite-difference time-domain method

In this paper we give a necessary and sufficient condition for the stabilit y of the finite-difference time-domain method (FDTD method). This is an exp licit time stepping method that is used for solving transient electromagnet ic field problems. A necessary (but not a sufficient) condition for its sta bility is usually obtained by requiring that discrete Fourier modes, define d on the FDTD grid, remain bounded as time stepping proceeds. Here we follo w a different approach. We rewrite the basic FDTD equations in tel ms of an iteration matrix and study the eigenvalue problem for this matrix. From th e analysis a necessary and sufficient condition for stability of the FDTD m ethod follows. Moreover, we show that for a particular time step the 2-norm of the FDTD iteration matrix is equal to the golden ratio. (C) 2000 Academ ic Press.