A Technique to Composite a Modified Newton's Method for Solving Nonlinear Equations

TL;DR

This paper introduces a new composite iterative method that combines classical root-finding techniques with a modified Newton's method, achieving higher efficiency in solving nonlinear equations.

Contribution

It proposes a novel composite approach that enhances convergence order while requiring only one function evaluation per iteration.

Findings

Achieves higher order of convergence than traditional methods.

Reduces computational effort by minimizing function evaluations.

Demonstrates improved efficiency index in numerical experiments.

Abstract

A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton's method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain root-finders with higher efficiency index.