New Efficient Steffensen Type method for Solving Nonlinear Equations

TL;DR

This paper introduces a derivative-free, fourth-order Steffensen-type method for solving nonlinear equations, which maintains high convergence order and outperforms existing methods based on numerical tests.

Contribution

The paper develops a new derivative-free Steffensen-type method by approximating derivatives with central differences, preserving convergence order and improving performance.

Findings

Method achieves fourth-order convergence without derivatives

Numerical tests show superior performance over existing methods

Method is efficient and easy to implement

Abstract

In the present paper, by approximating the derivatives in the Kou et al. \cite{Kou} fourth-order method by central difference quotient, we obtain new modification of this method free from derivatives. We prove the important fact that the method obtained preserve their order of convergence, without calculating any derivative. Finally, numerical tests confirm that our method give the better performance as compare to other well known Steffensen type methods.