A Comparative Analysis of Root-Finding Methods for Nonlinear Functions Using Python Programming Language

This research paper presents a comprehensive comparative analysis of root-finding methods for nonlinear functions using Python programming language. The study focuses on three widely used methods: Newton-Raphson, Secant, and Bisection, evaluating their performance in terms of accuracy, efficiency, and rate of convergence. Through empirical testing and analysis across various functions, including algebraic, exponential, and trigonometric functions, the paper examines the strengths and limitations of each method. The program utilizes two essential Python libraries: SymPy for symbolic computation, and Matplotlib for visualizing the convergence rates of various methods. Exception Handling is implemented to manage edge cases, ensuring the robustness of the program. The results demonstrate the varying efficiency of each method, with Newton-Raphson typically showing the fastest convergence, particularly in cases where the function is well-behaved near the root.