Numerical analysis for high-order six-stages split-step unconditionally-stable FDTD methods

High-order six-stages split-step unconditionally-stable finite-difference time-domain (FDTD) methods are presented. Along the positive and negative of the x, y, and z coordinate directions, the Maxwell´s matrix is split into six submatrices, and the time step is divided into six sub-steps. In addition, high-order central finite-difference operators are used to approximate the spatial differential operators first, and then the uniform formulation of the proposed high-order schemes is generalized. Subsequently, the analysis shows that all the proposed high-order methods are unconditionally stable, and the generalized form of the dispersion relations is carried out. Moreover, the effects of the mesh size, the time step and the order of schemes on the dispersion are illustrated through numerical results.