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ISSN: 1546-9239 (Print)
ISSN: 1554-3641 (Online)
Research Article Open Access

Solving Volterra's Population Model Using New Second Derivative Multistep Methods

K. Parand and G. Hojjati

Abstract

In this study new second derivative multistep methods (denoted SDMM) are used to solve Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential where the integral term represents the effect of toxin. This model is first converted to a nonlinear ordinary differential equation and then the new SDMM, which has good stability and accuracy properties, are applied to solve this equation. We compare this method with the others and show that new SDMM gives excellent results.

American Journal of Applied Sciences
Volume 5 No. 8, 2008, 1019-1022

DOI: https://doi.org/10.3844/ajassp.2008.1019.1022

Submitted On: 21 November 2007 Published On: 31 August 2008

How to Cite: Parand, K. & Hojjati, G. (2008). Solving Volterra's Population Model Using New Second Derivative Multistep Methods . American Journal of Applied Sciences, 5(8), 1019-1022. https://doi.org/10.3844/ajassp.2008.1019.1022

Open AccessCopyright: © 2008 K. Parand and G. Hojjati. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • multistep and multi-derivative methods
  • volterra's population model
  • integro-differential equation
  • stiff systems of ODEs