Comparison between Time Relaxed Monte Carlo Method and Majorant Frequency Scheme methods for the space homogeneous Boltzmann equation

Recently a new class of schemes, called Time Relaxed Monte Carlo (TRMC) has been introduced for the numerical solution of the Boltzmann equation of gas dynamics. The motivation is to propose a systematic framework to derive Monte Carlo methods effective near the fluid dynamic regime. Before the methods can be accepted as alternative tools to other methods, they have to show that they are able to reproduce results obtainable by well established reliable methods. In this paper a detailed comparison is performed between TRMC methods and the Majorant Frequency Scheme in the case of the space-homogeneous Boltzmann equation. In particular, the effect of finite number of particles is considered.