An improvement of two nonstandard finite difference schemes for two population mathematical models

Abstract

The aim of this paper is to design appropriate nonstandard finite difference (NSFD) schemes for two population mathematical models based on coupled nonlinear ordinary differential equations. Our work clarifies existing constructions of NSFD schemes for these two population models, which are not in full compliance with Mickens' methodology. We select the denominator functions for the discrete first-order derivatives depending on the existence of conservation laws, by following empirical rules suggested by Mickens. We fix nonlocal discretizations that preserve positivity of the schemes, irrespective of the value of the step size. Thus, our NSFD schemes are dynamically consistent with the two population models. We conduct a numerical study to assess the performance of the NSFD method.