Central schemes for balance laws of relaxation type

Several models in mathematical physics are described by quasi-linear hyperb olic systems with source term and in several cases the production term can become sti. Here suitable central numerical schemes for such problems are d eveloped and applications to the Broadwell model and extended thermodynamic s are presented. The numerical methods are a generalization of the Nessyahu-Tadmor scheme to the nonhomogeneous case by including the cell averages of the production t erms in the discrete balance equations. A second order scheme uniformly acc urate in the relaxation parameter is derived and its properties analyzed. N umerical tests con rm the accuracy and robustness of the scheme.