Higher Order FD-Padé Scheme for 3-D Parabolic Equation in Radio-Wave Propagation

This letter presents a higher order finite-difference (FD) and Padé approximations method for the three-dimensional (3-D) parabolic equation (PE) to predict radio-wave propagation. This method uses a fourth-order FD approximation of the differential operator in the transverse direction and a higher order Padé approximation of the operator in the propagation direction. The fourth-order FD and higher order Padé (4FDHP) method is then derived. The Leontovich impedance boundary for the 4FDHP method and boundary for the second-order FD and higher order Padé (2FDHP) method are also derived. The important problem of the propagation angle of the different approximations for the 3D-PE is investigated. Simulated results show that the proposed 4FDHP method achieves a larger propagation angle and higher accuracy than those of the 2FDHP method and the Mitchell-Fairweather alternative-direction-implicit method.