  A simple iterative approach for solving a set of implicit kinetic moment
equations is proposed. This implicit solve is a key component in the IMEX
discretization of the multi-species Bhatnagar-Gross-Krook (M-BGK) model with
nontrivial collision frequencies depending on individual species temperatures.
We prove that under mild time step restrictions, the iterative method generates
a contraction mapping. Numerical simulations are provided to illustrate results
of the IMEX scheme using the implicit moment solver.
