In this paper we consider the development of hybrid numerical methods for the solution of hyperbolic relaxation problems with multiple scales. The main ingredients in the schemes are a suitable merging of probabilistic Monte Carlo methods in non-stiff regimes with high resolution shock capturing techniques in stiff ones. The key aspect in the development of the algorithms is the choice of a suitable hybrid representation of the solution. After the introduction of the different schemes the performance of the new methods is tested in the case of the Jin-Xin relaxation system and the Broadwell model.
"Hybrid multiscale methods for hyperbolic problems I. Hyperbolic relaxation problems." Commun. Math. Sci. 4 (1) 155 - 177, March 2006.