Variants of Chebyshev’s Method with Optimal Order of Convergence

[[abstract]]In this paper, we derive a one-parameter family of Chebyshev’s method for finding simple roots of nonlinear equations. Further, we present a new fourth-order variant of Chebyshev’s method from this family without adding any functional evaluation to the previously used three functional evaluations. Chebyshev-Halley type methods are seen as the special cases of the proposed family. New classes of higher (third and fourth) order multipoint iterative methods free from second-order derivative are also derived by semi-discrete modifications of cubically convergent methods. Fourth-order multipoint iterative methods are optimal, since they require three functional evaluations per step. The new methods are tested and compared with other well-known methods on the number of problems