Extension of Newton-Steffenssen method by Gejji-Jafari decomposition Technique for solving nonlinear equations

TL;DR

This paper enhances the Newton-Steffenssen method for solving nonlinear equations by integrating the Gejji-Jafari decomposition technique, resulting in a potentially more efficient numerical approach.

Contribution

The paper introduces a novel extension of the Newton-Steffenssen method using the Gejji-Jafari decomposition, improving solution efficiency for nonlinear equations.

Findings

Numerical examples demonstrate improved efficiency.

The new method shows higher convergence speed.

Performance surpasses traditional methods.

Abstract

In this paper we extend Newton-Steffenssen method for solving nonlinear equations, introduced by Sharma [J.R. Sharma, A composite third order Newton-Steffenssen method for solving nonlinear equations, Appl. Math. Comput. 169 (2005), 242-246] by using the Gejji-Jafari decomposition technique. Several numerical examples are given to illustrate the efficiency and performance of this new method.