International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3903 2020 2020 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan Issam Issam Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, UAE Wael Mahmoud Mohammad Salameh Laboratory of Applied Mathematics and Modeling, Department of Mathematics, Faculty of Exact Sciences, University of Constantine 1, Constantine 25017, Algeria Issam Bendib Faculty of Computer Studies, Arab Open University, Saudi Arabia Ahmad A. Abubaker Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria Adel Ouannas Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box 2600, Irbid, Jordan; Jadara University Research Center, Jadara University, Jordan Abdallah Al Al-Husban This study investigates the finite-time stability (FTS) of the discrete Sel’kov-Schnakenberg reaction-diffusion (SSRD) system, a mathematical model capturing the interplay between local reactions and spatial diffusion. A novel discretization framework based on finite difference methods (FDM) is developed to transform the continuous reaction-diffusion (RD) system into a discrete counterpart, enabling detailed computational analysis. Sufficient conditions for FTS are derived using Lyapunov functions (LF) and eigenvalue-based methods, ensuring precise predictions of the system’s behavior. Numerical simulations validate theoretical findings, demonstrating the proposed methods’ practical applicability to scenarios such as chemical reactions, biological processes, and technological systems. The influence of system parameters, boundary conditions, and initial conditions on the dynamic behavior is systematically analyzed. This study contributes to the broader understanding of RD systems, addressing key challenges in stability analysis and offering a computationally efficient framework with implications for science and engineering. 2025 2025 155 166 10.54216/IJNS.260415 https://www.americaspg.com/articleinfo/21/show/3903