On generalization based on Bi et al. Iterative methods with eighth-order convergence for solving nonlinear equations

Abstract

The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub's conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency. © 2014 Taher Lotfi et al.