Analytical approximations and Pade approximants for Volterra's population model

In this paper, an analytic approximation for Volterra.'s model for populati on growth of a species in a closed system is presented. The nonlinear integ ro-differential model includes an integral term that characterizes accumula ted toxicity on the species in addition to the terms of the logistic equati on. The series solution method and the decomposition method are implemented independently to the model and to a related ODE. The Pade approximants, th at often show superior performance over series approximations, are effectiv ely used in the analysis to capture the essential behavior of the populatio n u(t) of identical individuals. (C) 1999 Elsevier Science Inc. All rights reserved.