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Nonstandard Finite Difference Schemes For solving A Modified Epidemiological Model For computer Viruses / Dang Quang A, Hoang Manh Tuan, Dang Quang Long // Tạp chí Tin học và Điều khiển học = Journal of Computer Science And Cybernetics . - 2018. - Page 171 - 185. - ISSN:


15 p.
Ký hiệu phân loại (DDC): 005.3
In this paper we construct two families of nonstandard finite difference (NSFD) schemes preserving the essential properties of a computer virus propagation model. such as positivity boundedness and stability. The first family of NSFD schemes is constructed based on the nonlocal discretization and has first order of accuracy. while the second one is based on the combination of a classical Range kutta method and selection of a nonstandard denominator function and it is of fourth order of accuracy. The theoretical study of these families of NSFD schemes is performed with support of numerical simulations. The numerical simulations confirm the accuracy and the efficiency of the fourth order NSFD schemes. They hint that the disease free equilibrium point is not only locally stable hut also globally stable. and then this fact is proved theoretically. The experimental results also show that the global stability of the continuous model is preserved.
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