In this work, a stable numerical algorithm proposed by Chung et al. for the time-domain Maxwell equations is generalized. The time-domain Maxwell equations are solved by expressing the transient behaviors in terms of the modified Laguerre polynomials, and then the original equations of the initial value and boundary value can be transformed into a series of problems independent of the time variable. In this case the method of finite difference （FD）, the finite element method （FEM）, the method of moment （MoM）, etc. or the combination of these methods can be used to solve the problems. Finally, a numerical model is provided for the scattering problem with perfect matched layer （PML） by using FD. The comparison between the results of the proposed method and FDTD is presented to verify the proposed new method.
