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Some variants of Halley’s method with memory and their applications for solving several chemical problems

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Abstract

In this paper, we develop some variants of the well-known Halley’s iterative method to solve nonlinear equations. The resulting methods are one-step methods, with and without memory, which use different number of functional evaluations per iteration. Those with memory have higher efficiency indexes than Newton’s scheme and also than many known optimal iterative procedures without memory. Their dependence on the initial estimation is studied by using real multidimensional dynamical techniques, showing their stable behavior. This is also checked with some numerical examples, that illustrate the performance of the proposed methods compared with other well-known schemes in the literature. For all the examples considered, that include chemical equilibrium problems, global reaction rates in packed bed reactors or continuous stirred tank reactors, the methods with memory reach the approximations to the roots, within the established tolerance, using fewer number of functional evaluations than their partners.

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Authors and Affiliations

  1. Scientific Computing Group, Universidad de Salamanca, Salamanca, Spain

    Higinio Ramos

  2. Escuela Politécnica Superior, Campus Viriato, 49022, Zamora, Spain

    Higinio Ramos

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

    Alicia Cordero & Juan R. Torregrosa

Authors
  1. Alicia Cordero
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  2. Higinio Ramos
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  3. Juan R. Torregrosa
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Correspondence to Alicia Cordero.

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This research was partially supported by Ministerio de Ciencia, Innovación y Universidades PGC2018-095896-B-C22 and by Generalitat Valenciana PROMETEO/2016/089.

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Cordero, A., Ramos, H. & Torregrosa, J.R. Some variants of Halley’s method with memory and their applications for solving several chemical problems. J Math Chem 58, 751–774 (2020). https://doi.org/10.1007/s10910-020-01108-3

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  • DOI: https://doi.org/10.1007/s10910-020-01108-3

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