A Study on Numerical Methods for Solving Differential Equations and Their Applications in Real World Modelling

Abstract: This paper explores the application of numerical methods for solving differential equations, which are important tools for modelling multiple real world systems. In many cases, finding exact analytical solutions is not possible especially for complex or nonlinear problems. Therefore, numerical techniques are used to obtain accurate approximate solutions. Common methods such as Euler’s Method, Improved Euler (heun’s) Method, and Runge Kutta Method are addressed in this study. This paper focuses on the exponential and logistic growth models due to their importance in analyzing population behavior under different resource conditions.which are commonly used in population studies and in situations involving limited resources. By performing numerical imitation and comparing results this paper shows how these models can be effectively checked using numerical methods. Overall, the paper highlights the role of numerical techniques in connecting theoretical concepts with practical problem solving.