An iterative method with quartic convergence for solving nonlinear equations (Q942360)

A new two-step and three-step iterative methods are derived for solving nonlinear equations, using terms up to fourth-order in the Taylor series and the iterative method proposed by \textit{M. A. Noor, K. I. Noor, S. T. Mohyud-Din} and \textit{A. Shabbir} [ibid. 183, No.~2, 1249--1255 (2006; Zbl 1113.65052)] and by \textit{V. Daftardar-Gejji} and \textit{H. Jafari} [J. Math. Anal. Appl. 316, No.~2, 753--763 (2006; Zbl 1087.65055)]. The authors also prove that the three-step iterative method has fourth-order convergence. Numerical results for several functions are presented illustrating the efficiency of the three-step iterative method.