Least squares approximation method for the solution of Hammerstein–Volterra delay integral equations

Abstract

In this paper, an efficient numerical method is developed for solving the Hammerstein–Volterra delay integral equations by least squares (LS) approximation method, which is based on a polynomial of degree n to compute an approximation to the solution of Hammerstein–Volterra delay integral equations. The convergence analysis of the approximation solution relative to the exact solution of the integral equation is proved and its accuracy is illustrated on two numerical examples. The study of this integral equation is important because it has as a particular case the variant of a mathematical model from epidemiology.