A family of higher order multi-point iterative methods based on power mean for solving nonlinear equations

Abstract

In this paper, we have presented a family of two-point fourth order, three-point sixth order and four-point twelfth order iterative methods without memory based on power mean using weight function. The family of fourth order methods is optimal in the sense of Kung-Traub hypothesis. In terms of computational point of view, our methods require three evaluations (one function and two first derivatives) to get fourth order, four evaluations (two functions and two derivatives) to get sixth order and five evaluations (three functions and two derivatives) to get twelfth order. Hence, these methods have high efficiency indices 1.587, 1.565 and 1.644 respectively. Few known results can be regarded as particular cases of our family of methods. Some numerical examples are tested to know the efficiencies of the methods which verify the theoretical results.