Extending Nonstandard Finite Difference Scheme for the SEIR Epidemic Model

Authors

  • Enkh-Amar Shagdar Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar 13330, Mongolia https://orcid.org/0000-0001-5305-2021
  • Batgerel Balt Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar 13330, Mongolia

DOI:

https://doi.org/10.5564/jimdt.v4i1.2657

Keywords:

Matrix exроnential, Conservation law

Abstract

When constructing a non-standard difference scheme for the differential equations, denominator of the discrete derivative is chosen as the functions depending on step-sizes on the computational grid or lattice. In other existing non-standard finite difference methods for SEIR epidemic model, those denominator functions have the same. The new scheme discussed in this article is characterized by the fact that the corresponding derivatives of the system of ordinary differential equations are replaced by different denominator functions depending on each equation. The proposed method has important property that conversation law. By numerical comparisons are confirmed that the accuracy of new method is better than that of standard and non-standard finite difference schemes(Mickens-type NSFD schemes with the same denominator functions).

Халдвар Тархалтын SEIR Загварыг Тооцоолох Стандарт Бус Ялгаварт Схем

Хураангуй: Дифференциал тэгшитгэлийг тооцоолох стандарт бус ялгаварт схемийг байгуулахдаа уламжлалыг илэрхийлэх ялгаварт харьцааны хуваарийг тоон торны алхамаас хамаарсан функц хэлбэрээр сонгон авдаг. Одоо ашиглагдаж буй халдвар тархалтын загваруудыг тооцоолох стандарт бус ялгаварт схемүүд нь ижил хуваарьтай байна. Энэхүү өгүүлэлд авч үзэж буй стандарт бус ялгаварт схем нь дифференциал тэгшитгэлүүдийн системийн уламжлалуудыг тэгшитгэл бүрээс нь хамааруулж өөр өөр хуваарьтай ялгаварт харьцаагаар сольж байгуулж байгаагаараа онцлог юм. Шинэ схемийн хувьд системийн хадгалагдах хууль биелэж байгааг батлав. Тоон туршилтыг стандарт схем болон стандарт бус ижил хуваарьтай ялгаварт схемтэй харьцуулахад шинэ схем илүү сайн ажиллаж байгааг харуулав.

Түлхүүр үгс: Матрицын экспоненциал, Хадгалагдах хууль

Abstract
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References

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Published

2022-12-26

How to Cite

Shagdar, E.-A., & Balt, B. (2022). Extending Nonstandard Finite Difference Scheme for the SEIR Epidemic Model. Journal of Institute of Mathematics and Digital Technology, 4(1), 16–24. https://doi.org/10.5564/jimdt.v4i1.2657

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