How to develop fourth and seventh order iterative methods?

Sanjay K. Khattri, Ioannis K. Argyros

The work contributes two new iterative methods of convergence orders four and seven for solving nonlinear equations. During each iteration, the fourth order method requests three functional evaluations while the seventh order method requests four functional evaluations. Computational results demonstrate that the methods are efficient and exhibit equal or better performance as compared with other well known methods and the classical Newton method.