  The over-relaxation approach is an alternative to the Jin-Xin relaxation
method (Jin and Xin [1]) in order to apply the equilibrium source term in a
more precise way (Coulette et al. [2, 3]). This is also a key ingredient of the
Lattice-Boltzmann method for achieving second order accuracy (Dellar [4]). In
this work we provide an analysis of the over-relaxation kinetic scheme. We
compute its equivalent equation, which is particularly useful for devising
stable boundary conditions for the hidden kinetic variables.
