Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model

Abstract

In this paper, we present two numerical collocation methods for approximating the solution of Volterra’s population model by utilizing auto-correlation functions of scaling functions of Daubechies wavelets. By using the properties of these functions, we compute the Volterra integral exactly at dyadic points, and then reduce the integro-differential population model to a system of algebraic equations. Our numerical results demonstrate the effectiveness and accuracy of these methods, and we compare our numerical results with other approaches described in the literature. Additionally, we investigate an error bound for our schemes.