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

Abstract

This letter presents a higher-order finite-difference (FD) and Padé approximations method for the three-dimensional (3D) parabolic equation (PE) to predict radio-wave propagation. This method uses a 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\boldsymbol {th}}$</tex-math></inline-formula> -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 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{th}$</tex-math></inline-formula> -order FD and higher-order Padé (4FDHP) method is then derived. The Leontovich impedance boundary for the 4FDHP method and boundary for the 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{nd}$</tex-math></inline-formula> -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 (MF-ADI) method.