Solving Volterra's Population Model Using New Second Derivative Multistep Methods
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.
Copyright: © 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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- multistep and multi-derivative methods
- volterra's population model
- integro-differential equation
- stiff systems of ODEs