A difference scheme for the equations mentioned in the title is proposed, investigated and numerically illustrated. The complex-valued equations describe the electric field and polarization in a closed cavity filled with a resonant two-level medium. The three equations are of diffusion-reaction type and obey several conservation laws. By a suitable choice of a three-level difference scheme and its starting values it is possible to obtain similar discrete conservation laws. Stability is proved in the sense of nonlinear stability of Ben-Yu Guo for bounded solutions and sufficiently small time step (both conditions being also necessary for successful practical computations).
In the numerical realisation, the multigrid algorithm is used for the solution of the equations corresponding to a fixed time level. As computational results, stationary laser intensity profiles are shown for several parameter values.