Abstract
The main purpose of this paper is to investigate the solution of general reaction–diffusion glycolysis system numerically. Glycolysis model demonstrates the positive solution as the unknown variables show concentration of chemical substances. Three numerical methods are used to solve glycolysis model. Two methods are well-known finite difference (FD) schemes and one is proposed FD scheme. The proposed scheme is explicit in nature. The main feature of the proposed FD scheme is to preserve the property of positivity retained by the glycolysis model. Results are compared with forward Euler explicit scheme and Crank Nicolson implicit scheme. All the attributes are verified by simulations.
Highlights
Several chemical reaction models are described in the form of differential equation
First Crank Nicolson implicit and forward Euler explicit finite difference (FD) schemes are considered for system (2)
Glycolysis reaction diffusion model is solved by two existing FD schemes, forward Euler explicit scheme and Crank Nicolson implicit scheme
Summary
Differential equations have wide applications in various engineering and science disciplines. In chemistry, several chemical reaction models are described in the form of differential equation.Glycolysis, a basic chemical reaction occurring in the cytosol is considered to be the typical example of metabolic pathway for cellular energy. The abundance of glycolysis make it one of the ancient metabolic pathways for providing energy via breakdown of glucose C6H12O6, into pyruvate, CH3COCOO− + H+. Several chemical reaction models are described in the form of differential equation. Glycolysis, a basic chemical reaction occurring in the cytosol is considered to be the typical example of metabolic pathway for cellular energy.. The abundance of glycolysis make it one of the ancient metabolic pathways for providing energy via breakdown of glucose C6H12O6, into pyruvate, CH3COCOO− + H+. C6H12O6 + 2NAD+ + 2ADP + 2P → 2pyruvic acid,. Sel’kov presented a basic model that makes it possible to explain qualitatively most experimental data on single-frequency oscillations in glycolysis and contains coupled first order differential equations.. Sel’kov presented a basic model that makes it possible to explain qualitatively most experimental data on single-frequency oscillations in glycolysis and contains coupled first order differential equations.12 These equations are u′1 = −u1 + σu2 + u21u2⎫⎪⎪
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