Optimal fourth order family of iterative methods

Sanjay K. Khattri, S. Abbasbandy

In this work, we construct a family of optimal fourth order iterative methods requiring three evaluations. During each iterative step, methods need evaluation of two derivatives and one function. According to the Kung and Traub conjecture an optimal iterative method without memory based on $3$ evaluations could achieve an optimal convergence order of $4$. The proposed iterative family of methods are especially appropriate for finding zeros of functions whose derivative is easy to evaluate. For example, polynomial functions and functions defined via integrals.