On Some Optimal Jarratt-Type Fourth Order Methods for Nonlinear Equations

Abstract

This research focuses on the problem of solving system of nonlinear equations by using numerical methods. We extend two-step Jarratt type iterative meth- ods with fourth order of convergence to solve system of nonlinear equations. The proposed methods does not require the evaluation of second or higher order Fréchet derivatives per iteration to proceed and reach fourth order of convergence. Convergence analysis of the new methods is also presented. Finally, numerical results illustrate the reliability and efficiency of the proposed methods.