Numerical Computations of Time-Dependent Auto-Catalytic Glycolysis Chemical Reaction-Diffusion System

A combined semi-discretized spectral matrix collocation algorithm based on (new) family of Krawtchouk polynomials is proposed to solve the time-dependent nonlinear auto-catalytic glycolysis reaction-diffusion system arising in mathematical chemistry. The first stage of the numerical algorithm is devoted to the Taylor series time advancement procedure yielding to a (linear and steady) system of ODEs. In the second stage and in each time frame, a matrix collocation technique based on the Krawtchouk polynomials is utilized to the resulting system of ODEs in an iterative manner. The results of the performed numerical experiments with Neumann boundary conditions are given to show the utility and applicability of the combined Taylor-Krawtchouk spectral collocation algorithm. The positive property of the glycolysis chemical model is sustained by the proposed algorithm and verified through comparisons with existing numerical methods in the literature. The combined technique is simple and flexible enough to easily produce the approximate solutions of diverse physical and applied models in engineering and science.