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

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 24
• Main Authors: Zafar, Zain Ul Abadin, Shah, Zahir, Ali, Nigar, Kumam, Poom, Alzahrani, Ebraheem O.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 17.08.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Boundary conditions; Chemical reactions; Computer simulation; Crank–Nicolson method; Difference and Functional Equations; Diffusion; Equilibrium nodes; Finite difference method; Forward Euler method; Functional Analysis; Lengyel–Epstein chemical reaction (LECR) model; Mathematical modeling; Mathematical models; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Qualitative research; Stability analysis; Steady state; Forward Euler method; Nonstandard finite difference method; Lengyel–Epstein chemical reaction (LECR) model; Mathematical modeling; Stability analysis; Equilibrium nodes; Crank–Nicolson method
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02877-6

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.