Daubechies Wavelet Scaling Function Approach to Solve Volterra's Population Model

Abstract

In this paper, we focus on a collocation approach based on Daubechies wavelet scaling functions for approximating the solution of Volterra’s model of population growth of a species with a closed system. We present that the integral and derivative terms, which appear in Volterra’s model of the population, will be computed exactly in dyadic points. Utilizing this collocation technique, Volterra’s population model reduces into a system of nonlinear algebraic equations. In addition, an error bound for our method will be explored. The numerical results demonstrate the applicability and accuracy of our method.