In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous model such as the conservation of the norm of the magnetization and the decay of the electromagnetic energy. Stability is proved under a suitable CFL condition. Some numerical results for the 1D model are presented.