Numerical solution features of Maxwell equations by FDTD method in the homogeneous and nonhomogeneous formulations

In this paper we investigate the features of the numerical FDTD solution of Maxwell’s equations formulated as 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 evaluating the correctness of the obtained solution is defined. The features of the numerical solution of homogeneous and nonhomogeneous Cauchy problems for different forms of initial configurations of electromagnetic fields and setting pulses are analyzed. Necessary and sufficient conditions of correctness of the obtained solutions are formulated.