All Title Author
Keywords Abstract

Publish in OALib Journal
ISSN: 2333-9721
APC: Only $99

ViewsDownloads

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

DOI: 10.4236/oalib.1107077, PP. 1-12

Subject Areas: Dynamical System

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

Full-Text   Cite this paper   Add to My Lib

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.

Cite this paper

Clemence-Mkhope, D. P. (2021). Dynamically Consistent NSFD Discretization of Some Productive-Destructive Population Models Satisfying Conservations Laws. Open Access Library Journal, 8, e7077. doi: http://dx.doi.org/10.4236/oalib.1107077.

References

[1]  Mickens, R.E. (1994) Nonstandard Finite Difference Models of Differential Equations. World Scientific, Singapore. https://doi.org/10.1142/2081
[2]  Mickens, R.E. (2005) Advances in the Applications of Nonstandard Finite Difference Schemes. World Scientific, Singapore. https://doi.org/10.1142/5884
[3]  Mickens, R.E. (2005) Nonstandard Finite Difference Schemes for Differential Equations. Journal of Difference Equations and Applications, 8, 823-847. https://doi.org/10.1080/1023619021000000807
[4]  Mickens, R.E. (2005) Dynamic Consistency: A Fundamental Principle for Constructing NSFD Schemes for Differential Equations. Journal of Difference Equations and Applications, 11, 645-653. https://doi.org/10.1080/10236190412331334527
[5]  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
[6]  Dimitrov D. and Kojouharov, H. (2007) Stability-Preserving Finite-Difference Methods for General Multi-Dimensional Autonomous Dynamical Systems. International Journal of Numerical Analysis and Modeling, 4, 280-290.
[7]  Dimitrov, D.T. and Kojouharov, H.V. (2008) Nonstandard Finite-Difference Methods for Predator-Prey Models with General Functional Response. Mathematics and Computers in Simulation, 78, 1-11. https://doi.org/10.1016/j.matcom.2007.05.001
[8]  Dimitrov, D.T. and Kojouharov, H.V. (2011) Dynamically Consistent Numerical Methods for General Productive-Destructive Systems. Journal of Difference Equations and Applications, 17, 1721-1736. https://doi.org/10.1080/10236191003781947
[9]  Wood, D.T., Dimitrov, D.T. and Kojouharov, H.V. (2015) A Nonstandard Finite Difference Method for n-Dimensional Productive-Destructive Systems. Journal of Difference Equations and Applications, 21, 240-254. https://doi.org/10.1080/10236198.2014.997228
[10]  Wood, D. and Kojouharov, H. (2015) A Class of Nonstandard Numerical Methods for Autonomous Dynamical Systems. Applied Mathematics Letters, 50, 78-82. https://doi.org/10.1016/j.aml.2015.06.008
[11]  Wood, D. (2015) Advancement and Applications of Nonstandard Finite Difference Methods. Ph.D. Thesis, University of Texas at Arlington.
[12]  Bairagi, N. and Biswas, M. (2016) A Predator-Prey Model with Beddington-DeAngelis Functional Response: A Non-Standard Finite Difference Method. Journal of Difference Equations and Applications, 22, 581-593.
[13]  Biswas, M. and Bairagi, N. (2017) Discretization of an Eco-Epidemiological Model and Its Dynamic Consistency. Journal of Difference Equations and Applications, 23, 860-877. https://doi.org/10.1080/10236198.2017.1304544
[14]  Quang, D.A. and Hoang, M.T. (2017) Nonstandard Finite Difference Schemes for a General Predator-Prey System. Journal of Computational Science, 36, 101015. https://arxiv.org/abs/1701.05663v1 https://doi.org/10.1016/j.jocs.2019.07.002
[15]  Saha, P., Bairagi, N. and Biswas, M. (2019) On the Dynamic Consistency of a Discrete Predator-Prey Model. arXiv preprint arXiv:1906.02513.
[16]  Mickens, R.E. (2007) Numerical Integration of Population Models Satisfying Conservation Laws: NSFD Methods. Journal of Biological Dynamics, 1, 427-436. https://doi.org/10.1080/17513750701605598
[17]  Mickens, R.E. and Washington, T.M. (2013) NSFD Discretizations of Interacting Population Models Satisfying Conservation Laws. Computers and Mathematics with Applications, 66, 2307-2316. https://doi.org/10.1016/j.camwa.2013.06.011

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal