Abstract
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.
