TWO EFFICIENT UNCONDITIONALLY-STABLE FOUR-STAGES SPLIT-STEP FDTD METHODS WITH LOW NUMERICAL DISPERSION

Abstract

Two e-cient unconditionally-stable four-stages split- step (SS) flnite-difierence time-domain (FDTD) methods based on controlling parameters are presented, which provide low numerical dispersion. Firstly, in the flrst proposed method, the Maxwell's matrix is split into four sub-matrices. Simultaneously, two controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into four sub-steps. The second proposed method is obtained by adjusting the sequence of the sub- matrices deduced in the flrst method. Secondly, the theoretical proofs of the unconditional stability and dispersion relations of the proposed methods are given. Furthermore, the processes of obtaining the controlling parameters for the proposed methods are shown. Thirdly, the dispersion characteristics of the proposed methods are also investigated, and numerical dispersion errors of the proposed methods can be decreased signiflcantly. Finally, to substantiate the e-ciency of the proposed methods, numerical experiments are presented.