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

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.