A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model
type: Item
instance of: scholarly article
title: A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model
zbMATH Open document ID: 1299.65302
DOI: 10.1155/2013/783069
author: Majid Tavassoli Kajani
author: Mohammad Maleki
author: Adem Kilicman
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: A new shifted Legendre-Gauss collocation method is proposed for the solution of Volterra's model for population growth of a species in a closed system. Volterra's model is a nonlinear integrodifferential equation on a semi-infinite domain, where the integral term represents the effects of toxin. In this method, by choosing a step size, the original problem is replaced with a sequence of initial value problems in subintervals. The obtained initial value problems are then step by step reduced to systems of algebraic equations using collocation. The initial conditions for each step are obtained from the approximated solution at its previous step. It is shown that the accuracy can be improved by either increasing the collocation points or decreasing the step size. The method seems easy to implement and computationally attractive. Numerical findings demonstrate the applicability and high accuracy of the proposed method.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6373086
Wikidata QID: Q59029244
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/783069
OpenAlex ID: W2138263645
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description: scientific article; zbMATH DE number 6373086