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

V. Candela and R. Peris

Applied Mathematics and Computation, 2019, vol. 350, issue C, 93-104

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.

Keywords: Iterative methods; Nonlinear equations; Order of convergence; Stability; Derivative free methods (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:350:y:2019:i:c:p:93-104

DOI: 10.1016/j.amc.2018.12.042

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