Application of the Jury test in stability analysis of an explicit fourth-order staggered FDTD method

At present, the research on high-order accurate finite-difference time-domain (FDTD) method for the solution of Maxwell´s equations is very popular. For example, an explicit fourth-order staggered FDTD method is proposed recently. However, to find out all roots of high-order characteristic polynomial equation for stability analysis is a very difficult task. In this paper, the Jury test in automatic control theory is introduced, which only use those coefficients of the characteristic polynomial equation for stability analysis instead of directly solving it. Such treatment can greatly simplify the procedure of stability analysis.