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We consider the development of high order asymptotic-preserving linearmultistep methods for kinetic equations and related problems. The methods arefirst developed for BGK-like kinetic models and then extended to the case ofthe full Boltzmann equation. The behavior of the schemes in the Navier-Stokesregime is also studied and compatibility conditions derived. We show that,compared to IMEX Runge-Kutta methods, the IMEX multistep schemes have severaladvantages due to the absence of coupling conditions and to the greatercomputational efficiency. The latter is of paramount importance when dealingwith the time discretization of multidimensional kinetic equations.

Implicit-explicit linear multistep methods for stiff kinetic equations