On the splitting method for the numerical solution of Boltzmann and lattice Boltzmann equations for gas flows in microsystems

The modification of the splitting method for single kinetic equation or for the system of kinetic equations with discrete velocities is considered. The modification is based on the iterative procedure for the implicit Euler approximation on the collision stage of the method. The optimization problem for the hybrid scheme for linear equation of an advection stage is solved. Reported results may be applied in fluid and gas dynamics problems for the flows in natural and mechanical microsystems.