Dynamically Consistent NSFD Discretization of Some Productive-Destructive Population Models Satisfying Conservations Laws

Abstract

In this article, two general construction methods of nonstandard finite difference (NSFD) models are considered for productive-destructive models that also satisfy conservation laws: one for productive-destructive (PD) and the other for conservative systems. It is observed that the general NSFD method for PD systems may not result in numerical models for such systems that are dynamically consistent with respect to the conservation laws. This is illustrated through two examples, with one satisfying a direct conservation law and the other a generalized conservation law. Alternative NSFD schemes that are dynamically consistent with respect to the conservation laws are constructed for these examples using the general method for conservative systems.