Basin of Attraction from Modification Variant of Chebyshev-Halley Methods

Abstract

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   0 and   1 eighth-order convergence for   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.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   0 and   1 eighth-order convergence for   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.