Numerov-Padé Scheme for the One-Way Helmholtz Equation in Tropospheric Radio-Wave Propagation

This letter is devoted to applying the higher order finite-difference approximations to the tropospheric radio-wave propagation problem. It is proposed to use the fourth-order approximation (Numerov discretization) of the transverse differential operator, and rational Padé approximations of the propagation operator. A discrete transparent nonlocal boundary condition that can take into account the modified refractive index of the troposphere has been constructed. An error analysis of the considered scheme with emphasis on tropospheric propagation has been carried out. A comparison with the existing finite-difference schemes and the split-step Fourier method has been performed. The effectiveness of the proposed approach has been shown.