Abstract: Effective management of solar energy systems is crucial for maximizing energy output and maintaining grid stability. This research presents a detailed analysis of a nonlinear system of ordinary differential equations (ODEs) that simulates the dynamics of energy supply, demand, and storage in a solar farm. The model takes into account key factors such as solar irradiance, temperature, battery storage, and maintenance costs, providing a comprehensive framework for understanding the complex interactions within solar energy systems. By utilizing the Adomian Decomposition Method (ADM), we solve the ODE system and examine the stability of equilibrium points by calculating the eigenvalues of the Jacobian matrix. The model is parameterized using real-world data from China, ensuring its practical relevance. Our study evaluates the convergence of approximate solutions and computes residual errors for different levels of approximation, demonstrating the accuracy and reliability of the ADM. The results indicate that the system exhibits stable equilibrium points under normal conditions based on real data. Furthermore, we prove the existence and uniqueness of solutions using the Picard-Lindelof theorem. Numerical simulations show that the ADM provides highly accurate solutions, with residual errors decreasing significantly as the number of iterations increases. Additionally, we employ a dynamical-numerical control method using the CESTAC and CADNA library to determine the optimal step of ADM, approximation, and error. This research contributes to the growing body of knowledge on solar energy systems by providing a theoretical framework for analyzing solar farm dynamics and offering practical insights for optimizing energy production and storage. The findings have significant implications for energy policymakers, engineers, and researchers working on renewable energy systems.

Biography: Prof. Samad Noeiaghdam, PhD of Applied Mathematics, Research Professor of Henan Academy of Sciences, Zhengzhou, China and Adjunct Faculty member of Saveetha School of Engineering, India. He was an Associate Professor of Irkutsk National Research Technical University, and a Senior Researcher in South Ural State University, Russia during 2019-2024. His main research interests are numerical analysis, solving mathematical models, energy system problems, load leveling in energy storage, supply and demand systems, MHD and heat and mass transfer problems. He has more than 190 publications including several high quality papers in top journals as well as books, chapters and conference papers. Because of his high level activities in research and contribution to mathematical advancement globally he has been acknowledged as one of the top 2% scientists by Stanford University. He is the member of editorial board and guest editor in various journals and special issues.