  We propose fully explicit projective integration and telescopic projective
integration schemes for the multispecies Boltzmann and Bhatnagar-Gross-Krook
(BGK) equations. The methods employ a sequence of small forward-Euler steps,
intercalated with large extrapolation steps. The telescopic approach repeats
said extrapolations as the basis for an even larger step. This hierarchy
renders the computational complexity of the method essentially independent of
the stiffness of the problem, which permits the efficient solution of equations
in the hyperbolic scaling with very small Knudsen numbers. We validate the
schemes on a range of scenarios, demonstrating its prowess in dealing with
extreme mass ratios, fluid instabilities, and other complex phenomena.
