EXISTENCE OF CONTINUOUS SOLUTIONS OF A PERTURBED LINEAR VOLTERRA INTEGRAL EQUATIONS

Abstract

In this paper we study the existence of continuous solutions on a compact interval of perturbed linear Volterra integral equations. The existence of such a solution is based on the well-known Leray–Schauder principle for a fixed point in Banach space. A special interest is devoted to the study of the uniqueness of continuous solution. Our numerical approach is based on a fixed point method and we apply quadrature rules to approximate the solution for the perturbed linear Volterra integral equations. The convergence of the numerical scheme is proved. Some numerical examples are given to show the applicability and accuracy of the numerical method and to validate the theoretical results.