COMPARATIVE ANALYSIS OF ORTHOGONAL POLYNOMIALS FOR SOLVING VOLTERRA INTEGRAL EQUATION MODEL OF BLOOD GLUCOSE DYNAMICS

Abstract

In this study, we solve Volterra-type blood glucose concentration model by using collocation approaches which employ four various types of orthogonal polynomial bases such as Lucas polynomials, Modified Boubaker Polynomials, Gegenbauer polynomials, and Touchard polynomials. To achieve this aim, we investigate the effect of these polynomial families on the numerical solution of the model under two different types of collocation points which are uniform points and Chebyshev-Gauss-Lobatto points. The proposed numerical method converts the original Volterra-type model into a system of algebraic equations in terms of the approximate expansion of the unknown blood glucose concentration function via proper polynomial expansions. The efficiency and accuracy of the proposed numerical method are tested according to absolute error, relative error, percentage error, residual error, and CPU time. Moreover, the numerical results of the method using the four different polynomial bases are compared to the exact solution of the model. The comparison between the solutions provides us the effect of the selection of the appropriate polynomial and collocation points on the efficiency and accuracy of the numerical solution. The findings of this study are supposed to present an effective spectral collocation technique for solving Volterra-type blood glucose concentration models.