The purpose of this work is to develop two new iterative methods for solving nonlinear equations which does not require any derivative evaluations. These composed formulae have seventh and eighth order convergence and desire only four function evaluations per iteration which support the Kung-Traub conjecture on optimal order for without memory schemes. Finally, numerical comparison is provided to show its effectiveness and performances over other similar iterative algorithms in high precision computation.
"New seventh and eighth order derivative free methods for solving nonlinear equations." Tbilisi Math. J. 10 (4) 103 - 115, September 2017. https://doi.org/10.1515/tmj-2017-0049