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A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations

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  • Candela, V.
  • Peris, R.

Abstract

In this paper we show a strategy to devise third order iterative methods based on classic second order ones such as Steffensen’s and Kurchatov’s. These methods do not require the evaluation of derivatives, as opposed to Newton or other well known third order methods such as Halley or Chebyshev. Some theoretical results on convergence will be stated, and illustrated through examples. These methods are useful when the functions are not regular or the evaluation of their derivatives is costly. Furthermore, special features as stability, laterality (asymmetry) and other properties can be addressed by choosing adequate nodes in the design of the methods.

Suggested Citation

  • Candela, V. & Peris, R., 2019. "A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 93-104.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:93-104
    DOI: 10.1016/j.amc.2018.12.042
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    References listed on IDEAS

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    1. Cordero, Alicia & Soleymani, Fazlollah & Torregrosa, Juan R. & Haghani, F. Khaksar, 2017. "A family of Kurchatov-type methods and its stability," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 264-279.
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    Cited by:

    1. Raudys R. Capdevila & Alicia Cordero & Juan R. Torregrosa, 2019. "A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.

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