  We present results of explicit asymptotic approximations applied to
neutrino--electron scattering in a representative model of neutrino population
evolution under conditions characteristic of core-collapse supernova explosions
or binary neutron star mergers. It is shown that this approach provides stable
solutions of these stiff systems of equations, with accuracy and timestepping
comparable to that for standard implicit treatments such as backward Euler,
fixed point iteration, and Anderson-accelerated fixed point iteration. Because
each timestep can be computed more rapidly with the explicit asymptotic
approximation than with implicit methods, this suggests that algebraically
stabilized explicit integration methods could be used to compute neutrino
evolution coupled to hydrodynamics more efficiently in stellar explosions and
mergers than the methods currently in use.
