Positivity and Conservation Properties of Some Integration Schemes for Mass Action Kinetics

The numerical schemes approximating chemical reactions according to the mass action law should reproduce at least two properties of the corresponding physical system: mass conservation and nonnegativity of the concentrations. This paper analyzes the equations of mass action kinetics providing a proof of the existence, uniqueness, and positivity of the solution under mild hypotheses on the reaction rate and the stoichiometric coefficients. We then consider some classic integration schemes in terms of conservation, positivity, and accuracy compared to schemes tailored for production-destruction systems, and propose an original scheme which guarantees conservation and nonnegativity of the solution and has order of convergence between 2 and 3.