Higher-order efficient class of Chebyshev-Halley type methods

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• 作者：Young Ik Kim^a ; Ramandeep Behl ; ^b ; ^{ramanbehl87@yahoo.in" class="auth_mail" title="E-mail the corresponding author} ; ^{behlr@ukzn.ac.za" class="auth_mail" title="E-mail the corresponding author} ; S.S. Motsa^b
• 关键词：Nonlinear equations ; Simple roots ; Chebyshev&ndash ; Halley ; Extraneous Fixed Points ; Basins of attraction
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：273
• 期：Complete
• 页码：1148-1159
• 全文大小：2249 K

文摘

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.