Unconditional Contractivity in the Maximum Norm of Diagonally Split Runge--Kutta Methods
SIAM Journal on Numerical Analysis
Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Positive numerical integration methods for chemical kinetic systems
Journal of Computational Physics
Scientific Computing with Ordinary Differential Equations
Scientific Computing with Ordinary Differential Equations
Applied Numerical Mathematics
A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems
Applied Numerical Mathematics
Analysis of a multirate theta-method for stiff ODEs
Applied Numerical Mathematics
On the positivity step size threshold of Runge--Kutta methods
Applied Numerical Mathematics
An asymptotic preserving scheme for the streamer simulation
Journal of Computational Physics
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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.