Geodesic
On application of the finite-difference Pad\'e approximation of the pseudo-differential parabolic equation to the tropospheric radio wave propagation problem
Numerical methods and programming, Tome 21 (2020) no. 4, pp. 405-419.

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This paper is devoted to the numerical simulation of electromagnetic wave propagation in an inhomogeneous troposphere. The study is based on the wide-angle generalizations of the parabolic wave equation. The finite-difference Pade approximation is used to approximate the propagation operator. It is important that, within the proposed approach, the Pade approximation is carried out simultaneously along with the longitudinal and transverse coordinates. At the same time, the proposed approach gives an opportunity to model an arbitrary tropospheric refractive index. The method does not impose restrictions on the maximum propagation angle. The comparison with the split-step Fourier method and the geometric theory of diffraction is discussed. The advantages of the proposed approach are shown.
Keywords: Helmholtz equation; parabolic equation; radio wave propagation; Pade approximation. 
@article{VMP_2020_21_4_a4,
     author = {M. S. Lytaev},
     title = {On application of the finite-difference {Pad\'e} approximation of the pseudo-differential parabolic equation to the tropospheric radio wave propagation problem},
     journal = {Numerical methods and programming},
     pages = {405--419},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_4_a4/}
}
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M. S. Lytaev. On application of the finite-difference Pad\'e approximation of the pseudo-differential parabolic equation to the tropospheric radio wave propagation problem. Numerical methods and programming, Tome 21 (2020) no. 4, pp. 405-419. http://geodesic.mathdoc.fr/item/VMP_2020_21_4_a4/