Crank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate

Allaberen Ashyralyev; Evren Hincal; Bilgen Kaymakamzade

doi:10.3934/mbe.2021438

Crank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate

Math Biosci Eng. 2021 Oct 15;18(6):8883-8904. doi: 10.3934/mbe.2021438.

Authors

Allaberen Ashyralyev^{1

2

3

4}, Evren Hincal^{1

2}, Bilgen Kaymakamzade^{1

2}

Affiliations

¹ Department of Mathematics, Near East University, Nicosia, Mersin 10, Turkey.
² Mathematics Research Center, Near East University, Nicosia, Mersin 10, Turkey.
³ Peoples' Friendship University of Russia (RUDN University), Ul Miklukho Maklaya 6, Moscow 117198, Russia.
⁴ Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan.

PMID: 34814327
DOI: 10.3934/mbe.2021438

Abstract

In this work, we study second order Crank-Nicholson difference scheme (DS) for the approximate solution of problem (1). The existence and uniqueness of the theorem on a bounded solution of Crank-Nicholson DS uniformly with respect to time step τ is proved. In practice, theoretical results are presented on four systems of nonlinear parabolic equations to explain how it works on one and multidimensional problems. Numerical results are provided.

Keywords: Bounded solution; epidemic models; realization in computer; system of nonlinear parabolic equations.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Epidemics*
Incidence