Structure Preserving Algorithms for Mathematical Model of Auto-Catalytic Glycolysis Chemical Reaction and Numerical Simulations

Abstract

This paper aims to develop positivity preserving splitting techniques for glycolysis reaction-diffusion chemical model. The positivity of state variables in the glycolysis model is an essential property that must be preserved for all choices of parameters. We propose two splitting methods that remain dynamically consistent with the continuous glycolysis reaction-diffusion model. The proposed methods converge to a true steady-state or fixed point under the given condition. On contrary to the classical operator splitting finite difference methods, we use nonstandard finite difference theory to propose a new class of operator splitting techniques.