Neutrosophic Enclosure of Roots in Newton - Raphson Method

Abstract

The Newton–Raphson method is one of the most widely used iterative techniques for approximating the roots of nonlinear equations. Classical method lacks an inherent mechanism to capture uncertainty and indeterminacy in the approximation process. In this paper, enclosure of roots in interval analysis is modified into neutrosophic enclosure and newton raphson method is applied. The neutrosophic certified root is found with an explicit quantified indeterminacy component and an excluded falsity region. As the iteration progresses, the indeterminacy measure reduces to zero, with a certified root in neutrosophic enclosure.