We present recently completed numerical analysis work on stability for a non-equilibrium system important for the applications in transport models with adsorption. The proof of stability relies on a combinaton of symmetrization and rescaling and choice of variables, from which stability for the new variables follows naturally. There is a nice associated framework in Hilbert spaces, which generalizes to multiple components and nonlinear problems. I will also present numerical results. This talk is based on on joint work with F. Patricia Medina.