Differential Equation on Astrophysics: A Fundamental Approach to Understanding Cosmic Structures and Their Dynamic Evolution

Abstract

When it comes to describing, analysing, and making predictions about the dynamics of cosmic occurrences, the use of differential equations is very important in the field of astrophysics, which is itself regulated by physical laws that are described in mathematics. Differential equations are an immensely helpful mathematical tool for explaining the dynamic structure of the cosmos. They can be used to describe anything from the formation of galaxies and stars to the curvature of spacetime and the propagation of gravity waves. This book provides a comprehensive and in-depth investigation of the fundamental role that ordinary and partial differential equations play in astrophysical issues. More specifically, it examines how these equations are used in the process of explaining the genesis, structure, and evolution of celestial bodies. On the basis of basic physical constants and validated astrophysical evidence, we conduct an in-depth analysis of both classical and modern models, including the Lane-Emden equation for star structure and the Friedmann equations for cosmic expansion. In addition, we make use of numerical solutions in order to confirm the theoretical models and determine the influence that dynamic factors like pressure, temperature, and energy density have on the structures of the universe we are studying. Through the use of analytical derivation and empirical inquiry, this study demonstrates how differential equations may be used as instruments for the purpose of prediction and explanation in contemporary applications of astrophysics. The discoveries highlight the paramount relevance of mathematics in the process of deciphering the physical cosmology of the universe and offer up new opportunities for the modelling and simulation of astrophysical phenomena in the future.