Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Populations and Evolution
2015-01-05 v2 Adaptation and Self-Organizing Systems
Abstract
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the original one regardless of the step-sizes used in numerical simulations, in opposition of the forward Euler method that shows numerical instabilities when the step size overcomes a critical value.
Cite
@article{arxiv.1201.0535,
title = {Non Standard Finite Difference Scheme for Mutualistic Interaction Description},
author = {Gianluca Gabbriellini},
journal= {arXiv preprint arXiv:1201.0535},
year = {2015}
}
Comments
12 pages, 4 figures