A two-parameter third-order family of methods for solving nonlinear equations

摘要

In this paper, we present a new two-parameter family of iterative methods for solving nonlinear equations which includes, as a particular case, the classical Potra and Pták third-order method. Per iteration the new methods require two evaluations of the function and one evaluation of its first derivative. It is shown that each family member is cubically convergent. Several examples are given to illustrate the performance of the family members.