A short proof of the unconditional stability of the ADI–FDTD scheme

Abstract- The original proof for unconditional stability of the ADI-FDTD scheme for 3-D Maxwell's equations was algebraically complex, and could only be carried out with the help of significant use of computer-aided algebra. We present here a much simpler proof, which can be done by hand in a page or two. Since the new proof is based on an energy estimate (rather than a Fourier argument), it is more amenable to generalizations (for ex. to variable coefficients and/or to different types of boundary conditions). Index Terms- Alternating direction implicit (ADI) technique, FDTD method, stability, unconditional stability. I