Families of Newton type methods for solving non-linear equations are obtained. These families consist of second and third order methods. Concrete two step methods are presented which are obtained as a unification of some existing methods in the literature and the standard secant method. It is shown that by this unification, the order of convergence of the methods increases. All the methods presented in this paper are well supported by examples.

Tbilisi Mathematical Journal, Vol. 5(1) (2012), pp. 17-29