Locally one-dimensional finite-difference scheme for the electrodynamic problems with given wavefront

The locally one-dimensional finite-difference scheme for three-dimensional Maxwell's equations is represented. The scheme destines for numerical solving of problems with initial data on the characteristic surface and has the second order of summary approximation in grid norm on uniform grids. Energy change theorem for presented scheme is the algebraic corollary of its equations, as the difference analogues of electromagnetic energy and Joule heat losses are the positive defined quadratic forms of grid functions of unknowns. This theorem guarantees convergence of difference solution to exact solution with the second order in the energy norm. The convergence speed is checked by the comparison with analytical solutions.