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CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior

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Abstract

A family of fourth-order iterative methods without memory, for solving nonlinear systems, and its seventh-order extension, are analyzed. By using complex dynamics tools, their stability and reliability are studied by means of the properties of the rational function obtained when they are applied on quadratic polynomials. The stability of their fixed points, in terms of the value of the parameter, its critical points and their associated parameter planes, etc. give us important information about which members of the family have good properties of stability and whether in any of them appear chaos in the iterative process. The conclusions obtained in this dynamical analysis are used in the numerical section, where an academical problem and also the chemical problem of predicting the diffusion and reaction in a porous catalyst pellet are solved.

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Authors and Affiliations

  1. Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022, Valencia, Spain

    Alicia Cordero, Lucía Guasp & Juan R. Torregrosa

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  1. Alicia Cordero
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  2. Lucía Guasp
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  3. Juan R. Torregrosa
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Corresponding author

Correspondence to Alicia Cordero.

Additional information

This is one of several papers published together in Journal of Mathematical Chemistry on the “Special Issue: CMMSE 2017”.

This research was partially supported by Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P and Generalitat Valenciana PROMETEO/2016/089.

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Cordero, A., Guasp, L. & Torregrosa, J.R. CMMSE2017: On two classes of fourth- and seventh-order vectorial methods with stable behavior. J Math Chem 56, 1902–1923 (2018). https://doi.org/10.1007/s10910-017-0814-0

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  • DOI: https://doi.org/10.1007/s10910-017-0814-0

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