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A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model


Kajani, Majid Tavassoli and Maleki, Mohammad and Kilicman, Adem (2013) A multiple-step Legendre-Gauss collocation method for solving Volterra's population growth model. Mathematical Problems in Engineering, 2013. art. no. 783069. pp. 1-6. ISSN 1024-123X


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.

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Official URL or Download Paper: http://www.hindawi.com/journals/mpe/2013/783069/

Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
DOI Number: https://doi.org/10.1155/2013/783069
Publisher: Hindawi Publishing Corporation
Keywords: Multi-step collocation; Volterra population; Nonlinear integro-differential equations; Population growth models; Semi-infinite domains; Systems of algebraic equations.
Depositing User: Umikalthom Abdullah
Date Deposited: 10 Sep 2014 08:38
Last Modified: 20 Sep 2015 23:51
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/783069
URI: http://psasir.upm.edu.my/id/eprint/30262
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