Numerical dynamics of nonstandard finite difference schemes for a computer virus propagation model

被引：0
作者：
Dang Q.A. [1 ]
Hoang M.T. [2 ]
机构：
[1] Centre for Informatics and Computing, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, Cau Giay, Hanoi
[2] Institute of Information Technology, Vietnam Academy of Science and Technology (VAST), 18 Hoang Quoc Viet, Cau Giay, Hanoi
来源：
International Journal of Dynamics and Control | 2020年 / 8卷 / 03期
关键词：
Computer virus model; Dynamic consistency; Global stability; Lyapunov function; Nonstandard finite difference schemes;
D O I：
10.1007/s40435-019-00604-y
中图分类号：
学科分类号：
摘要：
In this paper, we construct and analyze nonstandard finite difference (NSFD) schemes for a computer virus propagation model. We prove theoretically that the proposed NSFD schemes preserve essential qualitative properties of the continuous model. These properties are positivity and boundedness of solutions, equilibria and their stability properties. The performed numerical simulations support the theoretical results. The numerical experiments also show that standard finite difference schemes fail to preserve the essential properties of the continuous model for large step sizes. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
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页码：772 / 778
页数：6
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共 26 条
  • [11] Adekanye O., Washington T., Nonstandard finite difference scheme for a Tacoma Narrows Bridge model, Appl Math Model, 62, pp. 223-236, (2018)
  • [12] Dimitrov D.T., Kojouharov H.V., Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems, Appl Math Lett, 18, pp. 769-774, (2005)
  • [13] Dimitrov D.T., Kojouharov H.V., Stability-preserving finite-difference methods for general multi-dimensional autonomous dynamical systems, Int J Numer Anal Model, 4, pp. 280-290, (2007)
  • [14] Dimitrov D.T., Kojouharov H.V., Nonstandard finite-difference methods for predator–prey models with general functional response, Math Comput Simul, 78, pp. 1-11, (2008)
  • [15] Korpusik A., A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection, Commun Nonlinear Sci Numer Simul, 43, pp. 369-384, (2017)
  • [16] Wood D.T., Kojouharov H.V., A class of nonstandard numerical methods for autonomous dynamical systems, Appl Math Lett, 50, pp. 78-82, (2016)
  • [17] Dang Q.A., Hoang M.T., Dynamically consistent discrete metapopulation model, J Differ Equ Appl, 22, pp. 1325-1349, (2016)
  • [18] Dang Q.A., Hoang M.T., Lyapunov direct method for investigating stability of nonstandard finite difference schemes for metapopulation models, J Differ Equ Appl, 24, pp. 15-47, (2018)
  • [19] Dang Q.A., Hoang M.T., Complete global stability of a metapopulation model and its dynamically consistent discrete models, Qual Theory Dyn Syst, 18, pp. 461-475, (2019)
  • [20] Dang Q.A., Hoang M.T., Dang Q.L., Nonstandard finite difference schemes for solving a modified epidemiological model for computer viruses, J Comput Sci Cybern, 34, pp. 171-185, (2018)
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