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In this paper, the authors propose a finite difference time domain formulation for the study of wave propagation in magnetic substrates with non-uniform internal field distribution. In this formulation, the Landau-Lifshitz-Gilbert (LLG ) equation in terms of B instead of H is considered together with Maxwell's equations. Unlike in existing methods the LLG equation is not linearized. B, H and M are decomposed into dc and ac parts. The dc parts are found by the iterative method in A. Faranhi and A. Konrad (2005). A leap-frog scheme is used to update the ac components.