Study of Application Analyzing Methods Differential Equations

Author(s)	Dr. Ramesh Bhaskarrao Ghadge, Dr. Ramesh Bhaskarrao Ghadge
Country	India
Abstract	This paper explores a range of proposed methods for solving differential equations, emphasizing their theoretical foundations, practical applications, and comparative effectiveness. The methods under review include traditional analytical techniques, such as separation of variables and integrating factors, alongside more contemporary numerical approaches like finite difference methods, methods, and finite element analysis. The study also delves into recent advancements in algorithmic strategies, including machine learning and artificial intelligence-based methods, which offer promising alternatives for handling complex differential equations that are analytically intractable. Through a comprehensive analysis, this paper aims to provide insights into the strengths, limitations, and suitability of each method in various contexts, thereby aiding researchers and practitioners in selecting the most appropriate techniques for their specific applications. The findings underscore the evolving nature of differential equation solving methods and highlight future innovations in this critical area of study.
Keywords	Finite Difference Methods, Application of the Finite,Difference Method Solving,Differential Equations.
Field	Mathematics
Published In	Volume 7, Issue 4, July-August 2025
Published On	2025-08-14
DOI	https://doi.org/10.36948/ijfmr.2025.v07i04.53734
Short DOI	https://doi.org/g9w7gm

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