Universal Journal of Mathematics and Mathematical Sciences

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EFFICIENCY OF PERTURBATION ITERATION METHOD COMPARED TO EULER AND MATLAB APPROACHES FOR SOLVING A MATHEMATICAL MODEL OF BLOOD GLUCOSE AND INSULIN DURING PHYSICAL ACTIVITY

Authors

  • Mahamat Saleh DAOUSSA HAGGAR
  • Jean Marie Ntaganda

Keywords:

efficiency, comparison, perturbation iteration method, Euler method, Matlab approach, response, heart rate, alveolar ventilation, glucose, insulin, physical activity

DOI:

https://doi.org/10.17654/2277141724001

Abstract

A comparison of mathematical models of blood glucose and insulin based on perturbation iteration method, Euler method and Matlab approach based on Runge-Kutta is discussed. The description of perturbation iteration method for different order derivatives in the Taylor series expansion is presented and efficiency of this method is investigated. Due to heart rate and alveolar ventilation which control cardiovascular-respiratory system, the response of physical activity to the dynamics of glucose and insulin has been carried out by taking the values of determinant parameters of cardiovascular-respiratory system for a 30-year old woman performing walking, jogging and running  fast. The numerical results show that the trends of perturbation iteration method are very close to the other two methods. These  results are in good agreement with experimental data. Consequently, perturbation iteration method providing solutions in the form of an infinite series is efficient to solve mathematical models of ordinary differential equation.

Received: November 16, 2023
Accepted: March 20, 2024

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Published

2024-04-03

Issue

Vol. 20 No. 1 (2024)

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Articles

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How to Cite

EFFICIENCY OF PERTURBATION ITERATION METHOD COMPARED TO EULER AND MATLAB APPROACHES FOR SOLVING A MATHEMATICAL MODEL OF BLOOD GLUCOSE AND INSULIN DURING PHYSICAL ACTIVITY. (2024). Universal Journal of Mathematics and Mathematical Sciences, 20(1), 1-17. https://doi.org/10.17654/2277141724001

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