Author: Jonqobilov, J.T.

Annotation: This article analyzes the two main approaches to solving differential equations — analytical (exact) and numerical (approximate) methods. Analytical methods make it possible to obtain the solution of a differential equation in the form of an exact mathematical expression, whereas numerical methods are based on calculating approximate solutions for complex and nonlinear equations. The paper highlights the advantages, disadvantages, areas of application, and interconnection of both methods. In addition, the importance of numerical computations using modern computer programs (MATLAB, Maple, Python, Wolfram Mathematica) is discussed. As a result, it is substantiated that the combined use of analytical and numerical methods represents the most effective approach to obtaining both practical and theoretical solutions of differential equations.

Keywords: differential equation, analytical method, numerical method, Runge–Kutta method, Euler method, computer modeling, approximate solution.

Pages in journal: 600 - 604