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A new approach to wave oriented radio propagation modeling based on extended finite difference time domain (FDTD) methods has been developed. The new approach takes advantage of the fact that when a pulsed radio wave propagates over a long distance the significant pulse energy exists only over a small part of the propagation path at any instant of time. This allows the use of a relatively small FDTD computational mesh that exists only over a portion of the propagation path, moving along with the pulse energy. At the leading edge of the FDTD mesh inside the moving window the appropriate terrain and atmospheric material parameters are added to the mesh. At the trailing edge the terrain, foliage and atmosphere that has been left behind by the pulse is removed. Absorbing boundaries are used appropriately at the boundaries of the mesh. The potential savings over using a full FDTD mesh over the entire length of the propagation path are enormous. The proposed method promises to be the first full wave method applicable to radio propagation prediction calculations over long propagation paths. The moving window FDTD method has been applied to propagation over different types of irregular terrain. Comparisons with path loss measurements and ray-based methods show good accuracy and illustrate the advantages of a full wave method. Applications to foliage covered terrain have also been demonstrated.