Dynamical analysis of an iterative method with memory on a family of third-degree polynomials
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Other documents of the author: Campos, Beatriz; Cordero, Alicia; Torregrosa, Juan R.; Vindel, Pura
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comunitat-uji-handle2:10234/173364
comunitat-uji-handle3:10234/173369
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Title
Dynamical analysis of an iterative method with memory on a family of third-degree polynomialsDate
2022Publisher
AIMS PressISSN
2473-6988Bibliographic citation
Beatriz Campos, Alicia Cordero, Juan R. Torregrosa, Pura Vindel. Dynamical analysis of an iterative method with memory on a family of third-degree polynomials[J]. AIMS Mathematics, 2022, 7(4): 6445-6466. doi: 10.3934/math.2022359Type
info:eu-repo/semantics/articlePublisher version
http://www.aimspress.com/article/doi/10.3934/math.2022359Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we ... [+]
Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we accomplish a complete dynamical study of an iterative method with memory, the Kurchatov scheme, applied on a family of cubic polynomials. To reach this goal we transform the iterative scheme with memory into a discrete dynamical system defined on R2. We obtain a complete description of the dynamical planes for every value of parameter of the family considered. We also analyze the bifurcations that occur related with the number of fixed points. Finally, the dynamical results are summarized in a parameter line. As a conclusion, we obtain that this scheme is completely stable for cubic polynomials since the only attractors that appear for any value of the parameter, are the roots of the polynomial. [-]
Is part of
AIMS Mathematics, 2022, vol. 7, no 4Funder Name
Ministerio de Ciencia, Innovación y Universidades | Universitat Jaume I
Project code
MICIU/ICTI2017-2020/PGC2018-095896-B-C22 | UJI-B2019-18
Grant URL
http://dx.doi.org/10.13039/501100011033
Project title or grant
Diseño, análisis y estabilidad de procesos iterativos aplicados a las ecuaciones integrales y matriciales y a la comunicación aeroespacial
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