Numerical Solution of Volterra–Hammerstein Delay Integral Equations

Abstract

In this article, a new numerical scheme based on the Chelyshkov wavelets is presented for finding the numerical solutions of Volterra–Hammerstein delay integral equations arising in infectious diseases. First, properties of Chelyshkov polynomials and Chelyshkov wavelets are discussed. Then, integral and derivative operators of these wavelets are constructed, for first time. The Chelyshkov wavelets and their operators are used to reduce these integral equations to a system of algebraic equations, and again these algebraic systems have been solved numerically by Newton’s iterative scheme. Finally, the error analysis of the proposed method is investigated and its accuracy is illustrated on three numerical examples. Also the results achieved by Chelyshkov wavelets method have been compared with that of by the Bernoulli wavelets scheme and the B-spline wavelets scheme.