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The time-domain Green's function of the external region beyond a given boundary is an inherently discretized version of the impedance condition. It is incorporated within the framework of the FDTD as a single layer boundary condition, termed the Green's function method (GFM). The stability characteristics of this method are described. The analysis is based on the general representation of the method in matrix form, whose eigenvalues are investigated. This formulation helps detect and remove possible instabilities of the algorithm.