Higher-order efficient class of Chebyshev Halley type methods

作者：Kim Young Ik; Behl Ramandeep^*; Motsa S S

来源：Applied Mathematics and Computation, 2016, 273: 1148-1159.

DOI：10.1016/j.amc.2015.09.013

• Nonlinear equations
• Simple roots
• Chebyshev-Halley
• Extraneous Fixed Points
• Basins of attraction

Construction of two-point sixth-order methods for simple root is an ambitious and challenging task in numerical analysis. Therefore, the main aim of this paper is to introduce a new highly efficient two-point sixth-order class of Chebyshev-Halley type methods free from second-order derivative for the first time. Each member of the proposed class requires only four functional evaluations (viz, two evaluations of function f and two of first-order derivative f') per full iteration. A variety of concrete numerical examples illustrate that our proposed methods are more efficient and perform better than existing two-point/three-point sixth-order methods available in the literature. From their dynamical study, it has been observed that our proposed methods have better stability and robustness as compared to the other existing methods.

• 出版日期2016-1-15