On the convergence of a difference approximation of self-consistent system of Maxwell equations on a class of discontinuous solutions

The stability and convergence of a numerical solution of self- consistent problem if investigated, which appears when computing electromagnetic fields in the collection accelerator resonator. The corresponding group of Maxwell equations and relativistic Newton equation of motion is solved by the finite-difference method. Inhomogeneous domain Ω is considered. The finite number of a piecewise smooth lines of discontinuity of first derivatives of solution are assumed. Outside the discontinuity lines the first derivatives are continuously. It is shown that the natural restriction on the steps is sufficient for the stability of the finite-difference approximation of self-consistent problem