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Dynamical analysis of an iterative method with memory on a family of third-degree polynomials

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Dynamical analysis of an iterative method with memory on a family of third-degree polynomials

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dc.contributor.author Campos, Beatriz es_ES
dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.contributor.author Vindel, Pura es_ES
dc.date.accessioned 2023-02-24T19:01:17Z
dc.date.available 2023-02-24T19:01:17Z
dc.date.issued 2022 es_ES
dc.identifier.uri http://hdl.handle.net/10251/192068
dc.description.abstract [EN] 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 R-2. 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. es_ES
dc.description.sponsorship This paper is supported by the MCIU grant PGC2018-095896-B-C22. The first and the last authors are also supported by University Jaume I grant UJI-B2019-18. Moreover, the authors would like to thank the anonymous reviewers for their comments and suggestions. es_ES
dc.language Inglés es_ES
dc.publisher American Institute of Mathematical Sciences es_ES
dc.relation.ispartof AIMS Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Nonlinear equation es_ES
dc.subject Kurchatov's scheme es_ES
dc.subject Stability es_ES
dc.subject Dynamical plane es_ES
dc.subject Bifurcation es_ES
dc.subject Chaos es_ES
dc.subject Parameter line es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Dynamical analysis of an iterative method with memory on a family of third-degree polynomials es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3934/math.2022359 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJI//UJI-B2019-18/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Telecomunicación - Escola Tècnica Superior d'Enginyers de Telecomunicació es_ES
dc.description.bibliographicCitation Campos, B.; Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vindel, P. (2022). Dynamical analysis of an iterative method with memory on a family of third-degree polynomials. AIMS Mathematics. 7(4):6445-6466. https://doi.org/10.3934/math.2022359 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3934/math.2022359 es_ES
dc.description.upvformatpinicio 6445 es_ES
dc.description.upvformatpfin 6466 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 7 es_ES
dc.description.issue 4 es_ES
dc.identifier.eissn 2473-6988 es_ES
dc.relation.pasarela S\455037 es_ES
dc.contributor.funder Universitat Jaume I es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
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