This thesis consists in two parts: In the first part, we study the approximation of neutrino radiative transfer in core-collapse supernovae. In particular, we study the Isotropic Diffusion Source Approximation (IDSA). To do so, we first rederive the asymptotic limits used in this approximation using Hilbert and Chapman-Enskog expansions. We then show, using a model problem, that the coupling mechanism used in the IDSA can lead to unphysical solutions. We finally propose some corrections for the homogeneous sphere test case. In the second part, we introduce the framework of Fuzzy Domain Decomposition Methods (FDDMs). These methods are heterogeneous domain decomposition methods characterized by a time-dependent volumic adaptive coupling. We compare these methods with classical domain decomposition methods and quantify the approximation error for a simple class of 1D model using Matched Asymptotic Expansions (MAE). Finally, we formulate a time-dependent FDDM.