I will present a numerical scheme approximating a JinÐXin linear system with implicit equilibrium on a bounded domain. This scheme relaxes toward the asymptotic limit of the linear system. The main properties of the limiting scheme are that it does not require to invert the implicit function defining the manifold, and that it provides an accurate discretization of the boundary conditions. The motivation for writing such a scheme comes from a model arising in kidney physiology. This work was done with Nicolas Seguin.