A new general eighth-order family of iterative methods for solving nonlinear equations

In this work, we present a family of iterative methods for solving nonlinear equations. It is proved that these methods have convergence order 8. These methods require three evaluations of the function, and only use one evaluation of the first derivative per iteration. The efficiency of the method is tested on a number of numerical examples. On comparison with the eighth-order methods, the iterative methods in the new family behave either similarly or better for the test examples.