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CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems

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Abstract

The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods have been proposed in the literature. The evolution of these methods in terms of order of convergence implies the inclusion of a weight function for each case, showing an optimal fourth-order convergence, in the sense of Kung–Traub’s conjecture. The analysis of these new schemes is performed by means of complex dynamics. These methods are applied on the solution of the nonlinear Colebrook–White equation and the nonlinear system of the equilibrium conversion, both frequently used in Chemistry.

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  • 05 December 2019

    The original version of this article unfortunately contained an error in title. Unintentionally, the special issue title was presented in addition to the article’s title.

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Authors and Affiliations

  1. Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de La Paz, 137, 26006, Logroño, La Rioja, Spain

    Francisco I. Chicharro & Tobías H. Martínez

  2. Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022, València, Spain

    Alicia Cordero & Juan R. Torregrosa

Authors
  1. Francisco I. Chicharro
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  2. Alicia Cordero
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  3. Tobías H. Martínez
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  4. Juan R. Torregrosa
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Correspondence to Francisco I. Chicharro.

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This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER/UE) and Generalitat Valenciana PROMETEO/2016/089.

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Chicharro, F.I., Cordero, A., Martínez, T.H. et al. CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems. J Math Chem 58, 555–572 (2020). https://doi.org/10.1007/s10910-019-01085-2

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  • DOI: https://doi.org/10.1007/s10910-019-01085-2

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