Study on Determining the Blood Glucose Concentration During an Intravenous Injection Using Volterra Integral Equations
Ahmed A. Khidir *
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.
Waad I. Alfaifi
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.
Salihah L. Alsharari
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.
Ibtisam M. Alanazi
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.
Lujain S. Alyasi
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this study, the mathematical model for determining the blood glucose concentration during an intravenous injection has been solved throw Volterra integral equation and using Chebyshev spectral method. The method is based on the blending of the Chebyshev pseudo spectral method and its implementation procedure reduces the Volterra integral equation to a system of algebraic equations that are easy to solve. For the practical application of the method, a mathematical model in medical science for determining the blood glucose concentration during an injection has been solved. Tables and figures were generated to verify the accuracy and convergence of the method. The results demonstrate that the method is efficient, convergent and accurate to the exact solution.
Keywords: Numerical methods;, Chebyshev collocation method;, Volterra integral equations.