Root finding for non linear equation based on improvement Newton’s method / Nor Azni Shahari ... [et al.]

A root-finding process is a process for finding zeroes of continuous functions and provide approximations to the roots, which are represented as small isolating intervals or as floating-point integers. One of the most prevalent problems encountered in the root finding process is the rapidity of convergence rate to the actual root and the accuracy of the root approximation. However, the procedure is dependent on the initial estimate, neither stability nor convergence are guaranteed. Mathematicians and scientists have used Newton’s Method, an iterative methodology, for centuries to find the solution to nonlinear equations. While there is an alternative numerical method for determining the roots of nonlinear function, such as Secant methods and Bisection methods, the Newton’s Method is by far the most popular among academia and industry owing to its quick convergence rate. Based on many research publications, Newton’s Method converges quickly in comparison to the other methods (for example see: Akram and Ann (2015), Azure et al. (2019), Mehtre and Singh (2019)). This was clearly seen in the number of iterations taken by each of the methods to converge to the exact solution.