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We consider the development of exponential methods for the robust timediscretization of space inhomogeneous Boltzmann equations in stiff regimes.Compared to the space homogeneous case, or more in general to the case ofsplitting based methods, studied in Dimarco Pareschi (SIAM J. Num. Anal. 2011)a major difficulty is that the local Maxwellian equilibrium state is notconstant in a time step and thus needs a proper numerical treatment. We showhow to derive asymptotic preserving (AP) schemes of arbitrary order and inparticular using the Shu-Osher representation of Runge-Kutta methods we explorethe monotonicity properties of such schemes, like strong stability preserving(SSP) and positivity preserving. Several numerical results confirm ouranalysis.

Exponential Runge-Kutta schemes for inhomogeneous Boltzmann equations with high order of accuracy