Geodesic
Two difference schemes for the numerical solution of Maxwell’s equations as applied to extremely and super low frequency signal propagation in the Earth-ionosphere waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1656-1677 
O. I. Akhmetov; V. S. Mingalev; I. V. Mingalev; O. V. Mingalev; Yu. V. Fedorenko. Two difference schemes for the numerical solution of Maxwell’s equations as applied to extremely and super low frequency signal propagation in the Earth-ionosphere waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1656-1677. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a10/
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     title = {Two difference schemes for the numerical solution of {Maxwell{\textquoteright}s} equations as applied to extremely and super low frequency signal propagation in the {Earth-ionosphere} waveguide},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two explicit two-time-level difference schemes for the numerical solution of Maxwell’s equations are proposed to simulate propagation of small-amplitude extremely and super low frequency electromagnetic signals (200 Hz and lower) in the Earth-ionosphere waveguide with allowance for the tensor conductivity of the ionosphere. Both schemes rely on a new approach to time approximation, specifically, on Maxwell’s equations represented in integral form with respect to time. The spatial derivatives in both schemes are approximated to fourth-order accuracy. The first scheme uses field equations and is second-order accurate in time. The second scheme uses potential equations and is fourth-order accurate in time. Comparative test computations show that the schemes have a number of important advantages over those based on finite-difference approximations of time derivatives. Additionally, the potential scheme is shown to possess better properties than the field scheme.

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