Features of Numerical Solution of the Maxwell Equations by the FDTD Method in the Homogeneous and Inhomogeneous Formulations

We investigate the features of the numerical FDTD solution of the Maxwell equations, formulated as the Cauchy problems for the corresponding homogeneous and inhomogeneous systems of equations. It is shown that for the case of time-limited field sources, the Cauchy problem for an inhomogeneous system is equivalent to the corresponding Cauchy problem for a homogeneous system. The criterion for estimating the correctness of the obtained solution is formulated. The features of the numerical solution of the homogeneous and inhomogeneous Cauchy problems for different forms of initial configurations of electromagnetic fields and setting pulses are analyzed. The necessary and sufficient conditions for correctness of the obtained solutions are formulated.