Highly Accurate Methods for Solving One-Dimensional Maxwell Equations in Stratified Media

Earlier, a bicompact difference scheme was constructed for stationary and nonstationary Maxwell equations. Its stencil includes only one step of the spatial grid. A grid node is placed at each interface, and the other nodes may be placed arbitrarily. This scheme explicitly takes into account interface conditions on the interfaces. This makes it possible to compute generalized solutions with discontinuities of the solution and its derivatives. A novel spectral decomposition method is used for solving nonstationary problems that can take into account an arbitrary medium dispersion law. A new form of the bicompact scheme is proposed, which allows one to reduce the complexity of computations by a factor of four, which is a significant improvement. For the first time, a rigorous substantiation of the proposed scheme is given.