The explicit splitting scheme for Maxwell's equations

This paper presents a new explicit scheme for the numerical integration of Maxwell's equations in isotropic and anisotropic dielectrics and conductors, as well as in the plasma in the case of the Vlasov–Maxwell system. In this scheme, the electric and magnetic fields are calculated in the same time points in the same spatial grid nodes, and a splitting in spatial directions and physical processes has been used. Scheme is monotonic and has 2nd order accuracy in time and 3rd order accuracy in the spatial variables. The presented scheme allows us to use a much larger step of time integration in modeling the propagation of low-frequency signals in the ionosphere than the widely used method of finite differences in the time domain for the same accuracy.