Analysis of Solution of Numerical Problem Using Maxima and Python Software

Abstract: The goal of this research paper is to look into how well the Newton-Raphson method works for solving transcendental equations using two different computer programs, Python and Maxima. The Newton-Raphson method converges faster than the bisection method and Regular Falsi method. This is why this iterative method is often used to find the roots of functions with real values. We test the algorithm's speed, accuracy, and ease of use on two different platforms: Maxima, a computer algebra system and Python, a general-purpose programming language with strong numerical libraries. The study gives error analysis, convergence behavior and step-by-step instructions for solving a few selected nonlinear equations. The results show that both tools are good for analyzing numbers, but they have different advantages when it comes to computational control, flexibility, visualization and syntax simplicity. This comparative analysis helps scientists, engineers, teachers and students choose the right tools for solving mathematics problems in science and engineering.