A Modification of Newton Method for Solving Non-linear Equations

Abstract

A large number of complex problems in Mathematics and its related fields require the solution of non-linear equations. The Newton method and its early modifications belong to the simplest but not sufficiently efficient techniques for solving non-linear equations. A desired characteristic of an efficient method of solving non-linear equations is to obtain a root with minimum error (usually lower than the precision limit) and lower number of iterations. In this study, we propose two methods of solving non-linear equations (Proposed methods 1 and 2) through a modification of the Newton Raphson’s method with the forward and central difference approximations of the first derivative. The performance of the proposed methods are assessed along with an existing method (Secant Method) using three illustrations. The proposed method 2 outperformed the existing method (Secant method) and proposed method 1, yielding the lowest absolute relative approximate error and the least number of iterations when used to find the roots of the non-linear equations under consideration. The proposed methods 1 and 2 were found to be suitable alternatives for solving non-linear equations.