A simply constructed third-order modifications of Newton's method

In this paper, we present a simple and easily applicable approach to construct some third-order modifications of Newton's method for solving nonlinear equations. It is shown by way of illustration that existing third-order methods can be employed to construct new third-order iterative methods. The proposed approach is applied to the classical Chebyshev–Halley methods to derive their second-derivative-free variants. Numerical examples are given to support that the methods thus obtained can compete with known third-order methods.