  Modeling correctly the transport of neutrinos is crucial in some
astrophysical scenarios such as core-collapse supernovae and binary neutron
star mergers. In this paper, we focus on the truncated-moment formalism,
considering only the first two moments (M1 scheme) within the grey
approximation, which reduces Boltzmann seven-dimensional equation to a system
of $3+1$ equations closely resembling the hydrodynamic ones. Solving the M1
scheme is still mathematically challenging, since it is necessary to model the
radiation-matter interaction in regimes where the evolution equations become
stiff and behave as an advection-diffusion problem. Here, we present different
global, high-order time integration schemes based on Implicit-Explicit
Runge-Kutta (IMEX) methods designed to overcome the time-step restriction
caused by such behavior while allowing us to use the explicit RK commonly
employed for the MHD and Einstein equations. Finally, we analyze their
performance in several numerical tests.
