On the stability of spectral methods for the homogeneous Boltzmann equation

In this paper we introduce a new smoothed scheme derived from the spectral Fourier method for the homogeneous Boltzmann equation recently introduced in [14, 15]. More precisely we show that using suitable smoothing filters the method can be designed in such a way that the spectral solution remains positive in time and preserves the total mass. Several numerical examples are given to illustrate the previous analysis