Stability condition and numerical dispersion of fourth-order compact precise-integration time-domain method

In order to mitigate the numerical dispersion errors of the compact precise integration time-domain (CPITD) algorithm, the fourth-order CPITD [CPITD(4)] method is proposed recently which is based on the fourth-order finite-difference scheme and the precise integration technique. Both the stability condition and the numerical dispersion equation have been obtained. In this paper, the numerical dispersion characteristics of the CPITD(4) method, especially the improvement of the numerical dispersion by using the fourth-order finite-difference scheme are discussed in detail. It is found that the numerical dispersion errors of the CPITD(4) method are much less than those of the CPITD, compact finite-difference time-domain (CFDTD), and CFDTD(2,4) methods and can be made nearly independent of the time-step size. Furthermore, the numerical experiments validate the accuracy and the efficiency of the CPITD(4) method, and also verify our analysis of the numerical dispersion characteristics of the CPITD(4) method.