A theoretical analysis of numerical dispersion in the high-order finite-difference time-domain (FDTD) method with weighted Laguerre polynomials (WLPs) is proposed in this paper. According to the numerical dispersion relation for the two-dimensional (2-D) case, the numerical phase velocities relevant to the direction of wave propagation, grid discretization and time-scale factor are obtained. For a fixed relative error of the numerical phase velocity, the suitable sampling point density and time-scale factor can be determined. Compared with the low-order WLP-FDTD, the high-order one shows its good dispersion characteristics while a low sampling density is used. Three numerical examples are included to validate the effectiveness of the high-order scheme.
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