Third and Fourth-order iterative methods for solving systems of nonlinear equations

TL;DR

This paper extends third-order iterative methods to systems of nonlinear equations, aiming to improve convergence order efficiently using weighted methods and computational comparisons.

Contribution

It introduces a new third and fourth-order iterative method for systems of nonlinear equations with enhanced convergence and efficiency.

Findings

The new methods achieve the theoretical order of convergence.

Numerical results confirm the improved efficiency and convergence.

Comparison with traditional methods shows better performance.

Abstract

The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's method with minimum number of functional evaluations.To achieve this goal,we have used weighted method. Computational efficiency is compared not only traditional way but also recently introduced flops-like based concept. Finally numerical results are given to confirm theoretical order of convergence.