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Higher-order efficient class of Chebyshev–Halley type methods

Author

Listed:
  • Kim, Young Ik
  • Behl, Ramandeep
  • Motsa, S.S.

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.

Suggested Citation

  • Kim, Young Ik & Behl, Ramandeep & Motsa, S.S., 2016. "Higher-order efficient class of Chebyshev–Halley type methods," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1148-1159.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:1148-1159
    DOI: 10.1016/j.amc.2015.09.013
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    References listed on IDEAS

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    1. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "On developing a higher-order family of double-Newton methods with a bivariate weighting function," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 277-290.
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