On convergence of kinetically-consistent difference schemes of gas dynamics

In this paper the convergence of kinetically-consistent difference schemes of gas dynamics in Euler variables with sources (sinks) in the case of the ideal gas is investigated. The convergence of difference scheme is proved by means of energetical method. For the class of sufficiently smooth solutions of differential problem it is proved that the solution of the difference problem converges in the mesh norme $L_2$ and that the rate of convergence is $O(h^2)$.