A Study of the Interval Newton Method for Nonlinear Equations

Abstract

This paper presents a study of the Interval Newton Method, an important numerical technique for obtaining verified solutions of nonlinear equations. Unlike classical methods such as the Newton Raphson method, the Interval Newton Method provides guaranteed intervals containing the true roots. The paper introduces the fundamentals of interval arithmetic and derives the method using the Mean Value Theorem. Several numerical examples involving algebraic and transcendental equations are discussed to illustrate the efficiency and reliability of the method. The study shows that the Interval Newton Method produces accurate root enclosures with fast convergence and plays a significant role in verified numerical computation and scientific applications.