Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab

• Published in: IEEE access 2024, Vol.12, p.12370-12389
• Main Authors: Saqib, Muhammad, Akhtar, Farhan, Hasnain, Shahid, Abbas, Imran, Askar, Sameh, Farman, Muhammad
• Format: Article
• Language: English
• Subjects: Algorithms; Dynamic stability; Dynamical systems; Finite difference method; Finite volume method; Graphical representations; Grid generation (mathematics); Mathematical models; MATLAB; Model accuracy; Nonlinear differential equations; Nonlinear systems; Numerical methods; Qualitative analysis; Reaction-diffusion equations; Stability analysis; staggered grid approach; Systems analysis; time-dependent coupled reaction-diffusion model; Von Neuman stability analysis
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2024.3354812

In this research, we present two Numerical algorithms for studying the dynamics of spatially extended coupled nonlinear reaction-diffusion model. The difference in this work is to model a system of reacting and diffusing chemicals, and how to predict the dynamics of ecologically relevant behavior, including chaos. The goal can be achieved by applying a proposed staggered grid finite volume method for solving the Reaction model, rigorously validating the numerical method and grid generation techniques against established results. Additionally, we integrate an Alternating Direction Implicit formulation to compare the efficiency and accuracy of the model’s results. Dynamical system analysis, including linear stability analysis, is applied to comprehend the fundamental qualitative features of the inhibitor-activator system inherent in the coupled reaction-diffusion equations. Results, presented in tables and graphical representations, show that the schemes’ high accuracy at fourth-order precision in space and second-order in time, with conditional stability. Numerical results showed that the proposed finite volume approach was exceptionally proficient and accurate for tackling the two-dimensional nonlinear coupled reaction-diffusion model. Overall, the dialog highlights the significance of the proposed staggered grid finite approach and calculations for fathoming coupled reaction-diffusion equations are widely studied in biological and chemical systems of nonlinear differential equations.