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Dimitrov, D.T. and Kojouharov, H.V. (2006) Positive and Elementary Stable Nonstandard Numerical Methods with Applications to Predator-Prey Models. Journal of Computational and Applied Mathematics, 189, 98-108. https://doi.org/10.1016/j.cam.2005.04.003

has been cited by the following article:

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

  AUTHORS: Dominic P. Clemence-Mkhope

  KEYWORDS: NSFD Method, Conservation Laws, Dynamically Consistent, Productive-Destructive Systems

  JOURNAL NAME: Open Access Library Journal, Vol.8 No.4, April 30, 2021

  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.