Construction of the collision integral kernel for the nonlinear Boltzmann equation from its matrix elements

The methods for constructing the kernels of collision integrals emerging in the expansion of the non-linear Boltzmann kinetic equation in spherical harmonics are investigated. The techniques developed for calculating the kernel from the known matrix elements of the collision integral using the averaging over a number of computational parameters make it possible to substantially improve the accuracy of the proposed algorithm. In kernel calculations, Maxwell molecules were simulated using the asymptotic technique. This makes it possible to approximate the analytic expression of the kernel known in this case to a high degree of accuracy.