Numerical solutions of integral and integro-differential equations using Chebyshev polynomials of the third kind

Abstract

Our purpose in this study is to construct an algorithm based on the use of a finite expansion in Chebyshev polynomials of the third kind to solve singularly perturbed Volterra integral equations, first order integro-differential equations of Volterra type arising in fluid dynamics and Volterra delay integro-differential equations. The convergence of the method is investigated. Finally, some numerical experiments, which confirm the theoretical results, are shown and comparisons with other methods in literature are given.