Wild's sums and numerical approximation of nonlinear kinetic equations

We propose a numerical approximation to kinetic equations of Boltzmann type based on the splitting in time between the transport and the collision phases. By means of the representation of the solution to the relaxation part as an arithmetic mean of the convolution iterates of a quadratic positive operator, we construct a stable discretization valid for arbitrary values of the mean free path. Comparison of the present approximation with previous ones is made for Broadwell discrete velocity model.