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

被引：13

作者：

Zafar, Zain Ul Abadin ^{[1
]}

Shah, Zahir ^{[2
]}

Ali, Nigar ^{[3
]}

Kumam, Poom ^{[4
,5
]}

Alzahrani, Ebraheem O. ^{[6
]}

机构：

[1] Univ Cent Punjab, Fac Informat Technol, Lahore, Punjab, Pakistan

[2] King Mongkuts Univ Technol Thonburi KMUTT, Ctr Excellence Theoret & Computat Sci TaCS CoE, SCL Fixed Point Lab 802, Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok 10140, Thailand

[3] Univ Malakand, Dept Math, Dir Lower, Kpk, Pakistan

[4] King Mongkuts Univ Technol Thonburi KMUTT, Fac Sci, Dept Math, KMUTT Fixed Point Res Lab, Room SCL 802 Fixed Point Lab,Sci Lab Bldg, Bangkok 10140, Thailand

[5] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[6] King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

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; ASYMPTOTIC STABILITY; BIFURCATION;

D O I：

10.1186/s13662-020-02877-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：24

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