Mathematical Modelling for Nonlinear Glycolytic Oscillator

Nonlinear Glycolytic Oscillator

Authors

  • Zain Ul Abadin Zafar Faculty of Information and Technology, University of Central Punjab, Lahore, Pakistan

Keywords:

Glycolytic oscillator, NSFD method, RK4 method, chemical reaction

Abstract

Nowadays, numerical models have great importance in every field of science, especially for solving nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant species which interacts with other species is simulated by the Runge-Kutta of order four (RK4) and by the Non-Standard finite difference (NSFD) method. A NSFD model has been constructed for the biochemical reaction problems and numerical experiments were performed for different values of discretization parameter ‘h’. The results were compared with a well-known numerical scheme, i.e., RK4. The developed scheme NSFD gave better results than RK4

References

Keshat, L.E, Mathematical Models in Biology. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2005).

Sen, A.K. An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction. Journal of Mathematical Analysis and Applications 131: 232– 245 (1988).

Pongsumpun, P. Mathematical model of Dengue disease with incubation period of virus. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering 2(8): 535-539 (2008).

Zafar, Zain Ul Abadin, M. T. Hussain, A. Pervaiz, M. O. Ahmad & M. Kalim. A new fourth order compact difference scheme for one dimensional advection diffusion equation. Pakistan Journal of Science. 64: 359-362 (2012).

Zafar, Zain Ul Abadin, M.O. Ahmad, A. Pervaiz & M. Rafiq. Fourth Order Compact Method for One Dimensional Inhomogeneous Telegraph Equation with O(h4,k3). Pakistan Journal of Engineering and Applied Science 14: 96-101 (2014).

Mickens, R.E. Numerical integration of population models satisfying conservation laws: NSFD Methods. Biological Dynamics 1(4):1751-1766 (2007).

Mickens, R.E. Dynamical consistency: a fundamental principle for constructing Non-standard finite difference schemes for differential equations. Journal of Difference Equations and Applications, 13(4): 645-653 (2005).

Arafa, A.A.M., S.Z. Rida & M. Hegagi, An Application of the homotopy analysis method to the transient behavior of a biochemical reaction model. Information Science Letters 3(1): 29-33 (2014).

Edeki, S.O., E.A. Owoloko, A.S. Osheku, A.A. Opanuga, H.I. Okagbue & G.O. Akinlabi. Numerical Solutions of Nonlinear Biochemical model using a Hybrid Technique, International Journal of Mathematical Analysis 9(8): 403-416 (2015).

Brauer, F. & C.C. Chavez. Mathematical models in population biology and epidemiology. SpringerVerlag (2001).

Hashim, I., M.S.H. Chowdhury & S. Mawa. On multistage homotopy perturbation method applied to non-linear biochemical reaction model. Chaos Soltion and Fractals 16: 823-827 (2008).

d’Onofrio, A., P. Manfredi & E. Salinelli. Dynamic behavior of a discrete-time SIR model with information dependent vaccine uptake. Journal of Difference Equations and Applications 22(3): 485512 (2016).

Bairagi, N. & M. Biswas. A predator-prey model with Beddington-DeAngelis functional response: a non-standard finite differences method. Journal of Difference Equations and Applications, 22(4): 581593 (2016).

Zafar, Zain Ul Abadin, K. Rehan, M. Mushtaq & M. Rafiq. Numerical treatment for nonlinear Brusselator chemical model. Journal of Difference Equations and Applications 23(3): 521-538 (2017).

Zafar, Zain Ul Abadin, K. Rehan, M. Mushtaq & M. Rafiq. Numerical modelling for nonlinear biochemical reaction networks. Iranian Journal of Mathematical Chemistry 8(4): 413-423 (2017).

Zafar, Zain Ul Abadin, K. Rehan & M. Mushtaq. Fractional-order scheme for bovine babesiosis disease and tick population. Advances in Difference Equations 86: 1-19 (2017).

Zafar, Zain Ul Abadin, M. Mushtaq & K. Rehan. A non-integer order dengue internal transmission model, Advances in Difference Equations 23: 1-23 (2018).

Zafar, Zain Ul Abadin, K. Rehan & M. Mushtaq. HIV/AIDS epidemic fractional-order model. Journal of Difference Equations and Applications 23(7): 1298-1315 (2017).

Zafar, Zain Ul Abadin, M. Mushtaq, K. Rehan & M. Rafiq. Numerical simulations of fractional order Dengue disease with incubation period of virus. Proceedings of the Academy of Sciences: A. Physical and Computational Sciences 54(3): 277-296 (2017).

Zafar, Zain Ul Abadin, K. Rehan, M. Mushtaq & M. Rafiq. Fractional numerical treatment for biochemical reaction networks. Proceedings of the Academy of Sciences: A. Physical and Computational Sciences 54(3): 297-304 (2017).

Downloads

Published

2021-04-16

How to Cite

Zafar, Z. U. A. . (2021). Mathematical Modelling for Nonlinear Glycolytic Oscillator: Nonlinear Glycolytic Oscillator. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 55(1), 71–79. Retrieved from https://ppaspk.org/index.php/PPAS-A/article/view/201

Issue

Section

Articles