Exact Solution of a Bicompact Difference Scheme for Maxwell’s Equations

One-dimensional problems for Maxwell’s equations cover a wide variety of important application problems. Examples are problems in photonics, plasmonics, microwave technology, etc. For such problems, we earlier proposed a bicompact (two-point completely conservative) difference scheme. A exact solution of the corresponding system of discrete equations is constructed. It is applicable to problems in piecewise homogeneous media for an arbitrary configuration of volume and surface currents. Due to the constructed solution, the computational cost of solving such problems is reduced substantially.