In this paper, some sixth-order modifications of Jarratt method for solving single variable nonlinear equations are proposed. Per iteration, they consist of two function and two first derivative evaluations. The convergence analyses of the presented iterative methods are provided theoretically and a comparison with other existing famous iterative methods of different orders is given. Numerical examples include some of the newest and the most efficient optimal eighth-order schemes, such as Petkovic (SIAM J Numer Anal 47:4402–4414, 2010), to put on show the accuracy of the novel methods. Finally, it is also observed that the convergence radii of our schemes are better than the convergence radii of the optimal eighth-order methods.
Cordero, A., Hueso, J.L., Martinez, E., Torregrosa, J.R.: Efficient three-step iterative methods with sixth order convergence for nonlinear equations. Numer. Algor. 53, 485–495 (2010)MathSciNetMATHCrossRefGoogle Scholar