Approximated Solutions of Michaelis-Menten Diffusion Reaction Equation by Combination of Methods

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Published: 2023-09-25

Page: 132-146


Eli I. Cleopas

Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.

Avievie Igodo

Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.

Edikan E. Akpanibah *

Department of Mathematics and Statistics, Federal University Otuoke, Bayelsa, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

A lot of real life problems when modelled result to nonlinear differential equations. One example of such problems is the two point boundary nonlinear second order ordinary differential equation known as the Michaelis-Menten diffusion reaction equation. This equation cannot be solved easily by analytical methods; hence, there is need for numerical methods of solutions of this problem. In this paper, the fourth and sixth order approximated solutions of Michaeli’s-Menten diffusion reaction equation is obtained by a combination of Taylor series approximation with Ying Buzu Shu Algorithm and Taylor series approximation with Newton-Raphson method. The solutions by Ying Buzu Shu Algorithm and Newton-Raphson method were compared in terms of rate of convergence, error and relative error. Also, some numerical simulations were presented using matlab programming software. It was observed that a combination of Taylor series approximation with Ying Buzu Shu Algorithm has a faster rate of convergence, smaller error and relative error compared to the combination of Taylor series approximation with Newton-Raphson method.

Keywords: Newton-raphson method, michaelis-menten diffusion reaction equation, ying buzu shu algorithm, taylor series approximation


How to Cite

Cleopas , E. I., Igodo , A., & Akpanibah , E. E. (2023). Approximated Solutions of Michaelis-Menten Diffusion Reaction Equation by Combination of Methods. Asian Basic and Applied Research Journal, 5(1), 132–146. Retrieved from https://globalpresshub.com/index.php/ABAARJ/article/view/1867

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