The authors consider the Boltzmann type equations for a gas composed by four species of molecules with bimolecular chemical reactions and propose a numerical method based on a partition of the phase space of each molecule species into a large number of cells. Giving the coefficients of probability of chemical transions, one can construct a system of ordinary differential equations, of which the unknowns are the time-depending distribution of each species in each cell.
The authors give numerical results of the one-dimensional case (for the velocity), simulating only chemically reactive collisions and neglecting elastic ones. In these tests the test distribution functions are far from the Maxwellian.