Numerical study and stability of the Lengyel–Epstein chemical model with diffusion

Advances in Difference Equations

article

Zafar, Zain Ul Abadin¹  Shah, Zahir²  Ali, Nigar³  Kumam, Poom⁴  Alzahrani, Ebraheem O.⁶ 

[1] Faculty of Information Technology, University of Central Punjab;Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Mathematics, University of Malakand;KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Faculty of Science, King Abdulaziz University

关键词: Lengyel–Epstein chemical reaction (LECR) model;    Mathematical modeling;    Forward Euler method;    Stability analysis;    Crank–Nicolson method;    Equilibrium nodes;    Nonstandard finite difference method;   

DOI  :  10.1186/s13662-020-02877-6

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, a nonlinear mathematical model with diffusion is taken into account to review the dynamics of Lengyel–Epstein chemical reaction model to describe the oscillating chemical reactions. For this purpose, the dimensionless Lengyel–Epstein model with diffusion and homogeneous boundary condition is considered. The steady states with and without diffusion of the Lengyel–Epstein model are studied. The basic reproductive number is computed and the global steady states for the system are calculated. Numerical results are offered for two systems using three well known techniques to validate the main outcomes. The consequences established from this qualitative study are supported by numerical simulations characterized by distinct programs, adopting forward Euler method, Crank–Nicolson method, and nonstandard finite difference method.

【 授权许可】

CC BY