  We present a high-order, fully explicit, asymptotic-preserving projective
integration scheme for the nonlinear BGK equation. The method first takes a few
small (inner) steps with a simple, explicit method (such as direct forward
Euler) to damp out the stiff components of the solution. Then, the time
derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary
order. Based on the spectrum of the linearized BGK operator, we deduce that,
with an appropriate choice of inner step size, the time step restriction on the
outer time step as well as the number of inner time steps is independent of the
stiffness of the BGK source term. We illustrate the method with numerical
results in one and two spatial dimensions.
