Collocation Approximation Techniques for Solving Integro-
Differential Equations Via Shifted Chebyshev Polynomials
Author(s) : Ayinde Abdullahi Muhammed, Azeez Qowiyy Akinremi, Ishaq Ajimoti Adam, Ibrahim Salihu, Bello Akanbi Kareem, Owolanke Ayodele Olakiitan
ABSTRACT:
In this work, an approximate solution of linear second kind integro-differential equations of the Volterra and Fredholm types was studied utilizing shifted Chebyshev polynomials as basic functions. Additionally, the approximate solution was collocated using standard collocation and Chebyshev Gauss Lobatto collocation points, respectively. In terms of obtained errors, comparisons were done with the two collocation points. The performance of the method was demonstrated numerically in terms of the degree of approximation. Nonetheless, it was found that, Chebyshev Gauss-Lobatto collocation points exhibit better accuracy than standard collocation points, as can be seen from the tables of errors presented.
KEYWORD(S):
Approximate solution, Chebyshev Gauss-Lobatto, Shifted Chebyshev polynomials, Standard collocation, integro-differential equations.
