Application and Solution Methods of Differential Equations in Physical Modeling

Abstract

Differential equations are an important mathematical tool in physical modeling, playing a key role in describing various phenomena in nature. Ordinary differential equations, partial differential equations, and nonlinear differential equations are widely applied in fields such as classical mechanics, electromagnetism, heat conduction, and fluid dynamics to characterize the evolution of systems. For different physical systems, analytical methods, numerical methods, and modern computational techniques provide various approaches to solving differential equations, making the study of complex physical problems more efficient and accurate. This study focuses on the basic characteristics of different types of differential equations and their roles in physical modeling, analyzes the development of solution methods, and summarizes their specific applications in typical physical systems. Finally, the study looks forward to the development direction of differential equations in future physical research, aiming to provide theoretical references and practical guidance for related studies.