Stability analysis of finite-difference scheme for the system of kinetic equations

Stability analysis of the system of lattice Boltzmann equations for 1D diffusion with respect to initial conditions is performed. Stability condition is obtained by the method of first differential approximation with representation of the solution in form of travelling wave. It is showed that solutions of the system are asymptotically stable for all values of physical parameters. Stability condition is the same as for the system of lattice Boltzmann equations for modelling of hydrodynamical processes.