Abstract
In this paper, we extend the Mickens' methodology to construct a second-order nonstandard finite difference (NSFD) method, which preserves dynamical properties including positivity, local asymptotic stability and especially, global asymptotic stability of a general single-species model. This NSFD method is based on a novel weighted non-local approximation of the right-hand side function in combination with the renormalization of the denominator function. The weight guarantees the dynamic consistency and the nonstandard denominator function ensures the convergence of order 2 of the NSFD method. The result is that we obtain a second-order and dynamically consistent NSFD method. It is proved that the NSFD method is simple and efficient and can be extended for solving a broad range of mathematical models arising in real-world applications. Also, we combine the constructed second-order NSFD method with Richardson's extrapolation technique to generate high-order numerical approximations. Finally, the theoretical findings are illustrated and supported by numerical experiments.
Acknowledgments
We would like to thank the editor and anonymous referees for useful and valuable comments that led to a great improvement of the paper.
Authors' contributions
Manh Tuan Hoang: Conceptualization, Methodology, Software, Formal analysis, Writing- Original draft preparation, Methodology, Writing – Review & Editing, Supervision.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Availability of supporting data
The data supporting the findings of this study are available within the article [and/or] its supplementary materials.