In this paper, we present two new fifth-order iterative methods, namely the Newton-five α method and the Newton-five β method for solving a nonlinear equation. These new methods are shown to converge of the order five. We shall examine the effectiveness of these new Newton-type methods by approximating the simple root of a given nonlinear equation. The approximate solutions of the new Newton-type methods are stable, consistent and convergent.
Newton-five α, Newton-five β, Chebyshev third-order, Double Newton Fourth-order, Nonlinear equation, Order of convergence
