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Modeling correctly the transport of neutrinos is crucial in someastrophysical scenarios such as core-collapse supernovae and binary neutronstar mergers. In this paper, we focus on the truncated-moment formalism,considering only the first two moments (M1 scheme) within the greyapproximation, which reduces Boltzmann seven-dimensional equation to a systemof $3+1$ equations closely resembling the hydrodynamic ones. Solving the M1scheme is still mathematically challenging, since it is necessary to model theradiation-matter interaction in regimes where the evolution equations becomestiff and behave as an advection-diffusion problem. Here, we present differentglobal, high-order time integration schemes based on Implicit-ExplicitRunge-Kutta (IMEX) methods designed to overcome the time-step restrictioncaused by such behavior while allowing us to use the explicit RK commonlyemployed for the MHD and Einstein equations. Finally, we analyze theirperformance in several numerical tests.

Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations