Comparative Analysis of Bisection Method, Regula-Falsi, Method, and Newton–Raphson Method

<p><span lang="EN-US">This research paper presents a comparative analysis of three fundamental numerical methods for finding the roots of a real-valued function of a single variable: the Bisection method, Regula Falsi and the Newton- Raphson method. Real-valued functions of a single variable are fundamental tools with significant practical applications across numerous disciplines. Their importance stems from their ability to model and analyze real-world phenomena where one quantity depends on another. For example, analyzing and manipulating signals i.e. audio, video as functions of time, modeling the stress or strain on a material as a function of applied force. Relating pressure, volume, and temperature of a system, finding a function that best fits a set of data points, showing the relationship between a dependent and an independent variable. Real-valued functions of a single variable provide a fundamental language for describing how one measurable quantity changes in response to another. They allow us to build mathematical models, make predictions, analyze trends, and solve a wide range of practical problems across diverse fields. The study of these functions and the development of numerical methods to find their roots are crucial to tackle real-world problems that often don't have simple analytical solutions. The findings of this analysis provide valuable insights for practitioners in selecting the most appropriate numerical method for root-finding problems based on the specific characteristics of the function and desired level of accuracy.</span></p>