Basin of attraction from modification variant of Chebyshev-Halley methods

The development of Chebyshev-Halley Method for solving nonlinear equation is presented in this paper. Varian of Chebyshev-Halley method by Xiaojian (2008) was modified using Hermite Interpolation. The convergence analysis shows that these methods have sixth-order convergence for β = 0 and β = 1 eighth-order convergence for β = 1 2. The methods are classified by the order and efficiency index. Here, we considered other criteria, the basin of attractions which are presented for several examples.