On Chebyshev–Halley methods with sixth-order convergence for solving non-linear equations

Abstract

In this paper, we present a family of new variants of Chebyshev–Halley methods. The new methods have sixth-order convergence although they only add one evaluation of the function at the point iterated by Chebyshev–Halley methods. The numerical results presented show that the new methods work better not only in order but in efficiency.