Higher-order efficient class of Chebyshev–Halley type methods

Young Ik Kim, Ramandeep Behl and S.S. Motsa

Applied Mathematics and Computation, 2016, vol. 273, issue C, 1148-1159

Abstract: 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.

Keywords: Nonlinear equations; Simple roots; Chebyshev–Halley; Extraneous Fixed Points; Basins of attraction (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:1148-1159

DOI: 10.1016/j.amc.2015.09.013

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