Hybrid derivative-free methods for solving system of nonlinear equations

¹ Department of Mathematical Sciences, Bayero University, Kano, Nigeria
² Department of Mathematics, Sule Lamido University, Kafin Hausa, Nigeria
³ Department of Mathematics, Federal University, Dutse, Nigeria
⁴ Numerical Optimization Research Group, Bayero University, Kano, Nigeria

^* Corresponding author: abubakars.halilu@slu.edu.ng

Received: 14 December 2022
Accepted: 2 August 2023

Abstract

This work presents a predictor-corrector iterative approach for solving systems of nonlinear equations. The methods are derivative-free with correction and acceleration parameters obtained via approximating the Jacobian matrix. Using an inexact line search procedure and under appropriate conditions, we proved that the proposed method is globally convergent. We, additionally, present some numerical results to show the efficiency and effectiveness of the proposed method.