Algorithm for the Numerical Solutions of Volterra Population Growth Model with Fractional Order via Haar Wavelet

Haar wavelet method for Volterra population growth model with fractional order

Abstract

In this paper, a new collocation method based on the Haar wavelet is developed for the numerical solution of the fractional Volterra model (FVM) for the population growth of a species in a closed system. In the proposed method the derivative involved in the nonlinear model is approximated using Haar wavelet and the approximate expressions for the unknown function are obtained by the process of integration, the fractional derivative will be considered in the Caputo sense. The technique of residual correction, which aims to reduce the error of the approximate solution by estimating this error, is discussed in some detail. To show the computational efficiency of the proposed method, the residual correction technique is illustrated with an example. The numerical results are compared with existing methods from the literature. The numerical results show that the method is simply applicable, accurate, efficient, and robust.