On the Numerical Stability of Finite-Difference Time-Domain for Wave Propagation in Dispersive Media Using Quadratic Complex Rational Function

Abstract

Recently, based on a quadratic complex rational function, a simple and accurate finite-difference time-domain algorithm was introduced for the study of electromagnetic wave propagation in dispersive media. It is of great necessity to investigate the numerical stability of the quadratic complex rational function–finite-difference time-domain to fully utilize this finite-difference time-domain algorithm. In this work, using the von Neumann method with the Routh–Hurwitz criterion, the numerical stability conditions of the quadratic complex rational function–finite-difference time-domain are investigated. It is shown that the numerical stability conditions of the quadratic complex rational function–finite-difference time-domain are not same as those of the conventional finite-difference time-domain schemes.