Sixth-order and Seventh-order Iterative Methods for Solving Nonlinear Equations

TL;DR

This paper develops sixth- and seventh-order iterative methods, both derivative-based and derivative-free, for solving nonlinear equations, introducing weight functions for improved efficiency and flexibility.

Contribution

It presents new sixth- and seventh-order iterative families, including derivative-free variants, with weight functions for enhanced performance.

Findings

Constructed broad classes of sixth- and seventh-order methods

Introduced weight functions to improve efficiency

Provided flexible parametric combinations

Abstract

In this article, we discuss sixth-order and seventh-order iterative methods for nonlinear equations. Derivative-based and derivative-free, both categories are presented for said iterative methods. Especially sixth-order derivative-based and derivative-free iterative families are constructed in such a way that they circumstance a wide class of sixth-order methods which are developed in last many years. Weight functions are introduced to enhance the efficiency and parametric combination gives weight-age flexibility in between weight functions.