Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules

In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. order to avoid time step restrictions coming from convection term and small Knudsen number, combine approach with an implicit treatment relaxation term. We show how explicitly solve step, thus obtaining efficient stable any number. also derive explicit error estimate on convergence of proposed every fixed value