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

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

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Ramos, Higinio es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2021-03-12T04:31:39Z
dc.date.available 2021-03-12T04:31:39Z
dc.date.issued 2020-04 es_ES
dc.identifier.issn 0259-9791 es_ES
dc.identifier.uri http://hdl.handle.net/10251/163766
dc.description.abstract [EN] 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. es_ES
dc.description.sponsorship This research was partially supported by Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and by Generalitat Valenciana PROMETEO/2016/089. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Journal of Mathematical Chemistry es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Nonlinear equations es_ES
dc.subject One-point iterative root-solver with memory es_ES
dc.subject Halley's method es_ES
dc.subject Convergence order es_ES
dc.subject Efficiency index es_ES
dc.subject Stability analysis es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Some variants of Halley's method with memory and their applications for solving several chemical problems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10910-020-01108-3 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.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.rights.accessRights Cerrado 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.; Ramos, H.; Torregrosa Sánchez, JR. (2020). Some variants of Halley's method with memory and their applications for solving several chemical problems. Journal of Mathematical Chemistry. 58(4):751-774. https://doi.org/10.1007/s10910-020-01108-3 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s10910-020-01108-3 es_ES
dc.description.upvformatpinicio 751 es_ES
dc.description.upvformatpfin 774 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 58 es_ES
dc.description.issue 4 es_ES
dc.relation.pasarela S\423815 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.description.references J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Banach Spaces (Academic Press, New York, 1970) es_ES
dc.description.references M.S. Petkovic̀, B. Neta, L.D. Petkovic̀, J. Džunic̀, Multipoint methods for solving nonlinear equations (Elsevier, Amsterdam, 2013) es_ES
dc.description.references S. Amat, S. Busquier, Advances in Iterative Methods for Nonlinear Equations (Springer SIMAI, Switzerland, 2016) es_ES
dc.description.references J.F. Traub, Iterative Methods for the Solution of Equations (Chelsea Publishing Company, New York, 1997) es_ES
dc.description.references A. Cordero, J.M. Gutiérrez, Á.A. Magreñán, J.R. Torregrosa, Stability analysis of a parametric family of iterative methods for solving nonlinear models. Appl. Math. Comput. 285, 26–40 (2016) es_ES
dc.description.references C. Amorós, I.K. Argyros, R. González, Á.A. Magreñán, L. Orcos, I. Sarría, Study of a high order family: local convergence and dynamics. Mathematics 7(3), 14 (2019) es_ES
dc.description.references F.I. Chicharro, A. Cordero, J.R. Torregrosa, Drawing dynamical and parameters planes of iterative families and methods. Sci. World 2013, 11 (2013) es_ES
dc.description.references S. Amat, S. Busquier, C. Bermúdez, Á.A. Magreñán, On the election of the damped parameter of a two-step relaxed Newton-type method. Nonlinear Dyn. 84(1), 9–18 (2016) es_ES
dc.description.references B. Neta, The basins of attraction of Murakami’s fifth order family of methods. Appl. Numer. Math. 110, 14–25 (2016) es_ES
dc.description.references B. Campos, A. Cordero, J.R. Torregrosa, P. Vindel, A multidimensional dynamical approach to iterative methods with memory. Appl. Math. Comput. 271, 701–715 (2015) es_ES
dc.description.references B. Campos, A. Cordero, J.R. Torregrosa, P. Vindel, Stability of King’s family of iterative methods with memory. Comput. Appl. Math. 318, 504–514 (2017) es_ES
dc.description.references A.M. Ostrowski, Solution of Equations and Systems of Equations (Academic Press, New York, 1960) es_ES
dc.description.references T.R. Scavo, J.B. Thoo, On the geometry of Halley’s method. Am. Math. Mon. 102, 417–426 (1995) es_ES
dc.description.references A. Melman, Geometry and convergence of Euler’s and Halley’s methods. SIAM Rev. 39(4), 728–735 (1997) es_ES
dc.description.references S. Amat, S. Busquier, J.M. Gutiérrez, Geometric constructions of iterative functions to solve nonlinear equations. Comput. Appl. Math. 157, 197–205 (2003) es_ES
dc.description.references P. Blanchard, Complex analytic dynamics on the Riemann sphere. Bull. AMS 11(1), 85–141 (1984) es_ES
dc.description.references R.C. Robinson, An Introduction to Dynamical Systems, Continous and Discrete (American Mathematical Society, Providence, 2012) es_ES
dc.description.references J.P. Jaiswal, A new third-order derivative free method for solving nonlinear equations. Univ. J. Appl. Math. 1(2), 131–135 (2013) es_ES
dc.description.references A. Cordero, J.L. Hueso, E. Martínez, J.R. Torregrosa, Steffensen type methods for solving nonlinear equations. Comput. Appl. Math. 236, 3058–3064 (2012) es_ES
dc.description.references A. Cordero, J.R. Torregrosa, Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007) es_ES
dc.description.references H. Ramos, J. Vigo-Aguiar, The application of Newton’s method in vector form for solving nonlinear scalar equations where the classical Newton method fails. Comput. Appl. Math. 275, 228–237 (2015) es_ES
dc.description.references A. Constantinides, N. Mostoufi, Numerical methods for chemical engineers with MATLAB applications (Prentice-Hall, Englewood Cliffs, 1999) es_ES


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