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This paper investigates the representation of the dielectric boundary and the absorbing boundary conditions (ABC) that are major concerns in the nonstandard FDTD (NS-FDTD) method. The effective permittivity model of the dielectric boundary is examined and it is found that its accuracy decreases when the boundary coincides with a node. To overcome this difficulty, we propose an alternative, highly accurate boundary model based on an analytic boundary condition. The accuracy of Berenger's split-field perfectly matched layer (PML) as an ABC is also demonstrated for the NS-FDTD algorithm.