An implicit FDTD scheme for the propagation of VLF–LF radio waves in the Earth–ionosphere waveguide

A new finite-difference time-domain scheme is presented for the propagation of VLF–LF radio waves in the Earth–ionosphere waveguide. The new scheme relies on the implicit solution of the auxiliary equation that governs the current density in the ionosphere. The advantages and drawbacks of the new scheme are discussed. Its main advantage is its stability condition, which is the same as that of the FDTD method in a vacuum. This permits the time step of the calculation to be increased and then the overall computational time to be reduced. Numerical experiments demonstrate the accuracy of the new scheme and the reduction of the computational time.