Open AccessCrank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate
Author(s) -
Allaberen Ashyralyev,
Evren Hınçal,
Bilgen Kaymakamzade
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021438
Subject(s) - mathematics , uniqueness , nonlinear system , bounded function , crank–nicolson method , crank , parabolic partial differential equation , scheme (mathematics) , mathematical analysis , work (physics) , partial differential equation , geometry , mechanical engineering , physics , quantum mechanics , cylinder , engineering
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 $ \tau $ 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.