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Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods

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Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods

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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 2021-01-19T04:32:53Z
dc.date.available 2021-01-19T04:32:53Z
dc.date.issued 2019 es_ES
dc.identifier.issn 1392-6292 es_ES
dc.identifier.uri http://hdl.handle.net/10251/159367
dc.description.abstract [EN] In this paper, we study the dynamics of an iterative method based on the Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations. As it was proven in "A new family of iterative methods widening areas of convergence, Appl. Math. Comput.", this family has the property of getting good estimations of the solution when Newton's method fails. Moreover, the set of converging starting points for several non-polynomial test functions was plotted and they showed to be wider in the case of proposed methods than in Newton's case, for small values of the parameter. Now, we make a complex dynamical analysis of this parametric class in order to justify the stability properties of this family. es_ES
dc.description.sponsorship This research was supported by Spanish Ministry grant MTM2014-52016-C02-2-P, Generalitat Valenciana PROMETEO/2016/089 and UJI project P1.1B20115-16. The authors also want to thank the anonymous referees for their suggestions and comments that have improved the final version of the paper. es_ES
dc.language Inglés es_ES
dc.publisher Vilnius Gediminas Technical University es_ES
dc.relation.ispartof Mathematical Modelling and Analysis es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Nonlinear problems es_ES
dc.subject Iterative methods es_ES
dc.subject Complex dynamics es_ES
dc.subject Dynamical and parameter planes es_ES
dc.subject Critical points es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3846/mma.2019.021 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UJI//P1.1B20115-16/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-52016-C2-2-P/ES/DISEÑO DE METODOS ITERATIVOS EFICIENTES PARA RESOLVER PROBLEMAS NO LINEALES: CONVERGENCIA, COMPORTAMIENTO DINAMICO Y APLICACIONES. ECUACIONES MATRICIALES./ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vindel, P. (2019). Dynamical analysis to explain the numerical anomalies in the family of Ermakov-Kalitkin type methods. Mathematical Modelling and Analysis. 24(3):335-350. https://doi.org/10.3846/mma.2019.021 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3846/mma.2019.021 es_ES
dc.description.upvformatpinicio 335 es_ES
dc.description.upvformatpfin 350 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 24 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\393529 es_ES
dc.contributor.funder Universitat Jaume I es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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