Numerical methods for the problems of a difracting light beams propa gation in chemically active gases with thermal diffusion

In the present paper nonlinear conservative finite difference scheme for interaction of a laser beam with two component chemical gas in the case of difraction and self-influence of laser radiation as well as thermal diffusion of gas components are suggested. The existance of bounded and unity solution of finite difference scheme and its convergence to enough smooth solution of the differential problem are proved.