A class of iterative methods for solving nonlinear equation with fourth-order convergence

TL;DR

This paper introduces a new class of iterative methods with fourth-order convergence for solving nonlinear equations, improving efficiency by building on existing third-order methods and using weight functions.

Contribution

The paper develops a novel class of optimal fourth-order iterative methods based on third-order methods and weight functions for solving nonlinear equations.

Findings

Methods demonstrate higher convergence order

Physical examples show improved efficiency

Performance surpasses existing methods

Abstract

In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate the efficiency and performance of our method.