On some third-order iterative methods for solving nonlinear equations

Using the iteration formulas of second order [Mamta, V. Kanwar, V.K. Kukreja, Sukhjit Singh, On a class of quadratically convergent iteration formulae, Appl. Math. Comput. 2004, in press] for solving single variable nonlinear equations, two classes of third-order multipoint methods without using second derivative are derived. The main advantage of these classes is that they do not fail if the derivative of the function is either zero or very small in the vicinity of the required root. Further, a new family of Secant-like method with guaranteed super linear convergence is obtained by discrete modifications and their comparison with respect to the existing classical methods is given.