Finite difference schemes of the 4th order of approximation for Maxwell's equations

In this paper, optimum differential schemes for the solution of the Maxwell equations with the use of the Laquerre spectral transformation are considered. Additional parameters are introduced into the differential scheme of equations for harmonics. Numerical values of these parameters are obtained by minimization of an error of differential approximation of the Helmholtz equation. The optimum values of parameters thus obtained are used when constructing differential schemes — optimum differential schemes. Two versions of optimum differential schemes are considered. It is shown that the use of optimum differential schemes leads to an increase in the accuracy of the solution of the equations. A simple modification of the differential scheme gives an increase in the efficiency of the algorithm.