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Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p>5

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Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p>5

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Jordan-Lluch, Cristina es_ES
dc.contributor.author Sanabria-Codesal, Esther es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2019-06-01T20:01:19Z
dc.date.available 2019-06-01T20:01:19Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0377-0427 es_ES
dc.identifier.uri http://hdl.handle.net/10251/121415
dc.description.abstract [EN] It is known that the concept of optimality is not defined for multidimensional iterative methods for solving nonlinear systems of equations. However, usually optimal fourth order schemes (extended to the case of several variables) are employed as starting steps in order to design higher order methods for this kind of problems. In this paper, we use a non optimal (in scalar case) iterative procedure that is specially efficient for solving nonlinear systems, as the initial steps of an eighth-order scheme that improves the computational efficiency indices of the existing methods, as far as the authors know. Moreover, the method can be modified by adding similar steps, increasing the order of convergence three times per step added. This kind of procedures can be used for solving big-sized problems, such as those obtained by applying finite differences for approximating the solution of diffusion problem, heat conduction equations, etc. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and Fisher's equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the proposed schemes. (C) 2017 Elsevier B.V. All rights reserved. es_ES
dc.description.sponsorship This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P, MTM2015-64013-P and Generalitat Valenciana PROMETEO/2016/089. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation MINECO/MTM2015-64013-P es_ES
dc.relation MINECO/MTM2014-52016-C2-2-P es_ES
dc.relation GV/PROMETEO/2016/089 es_ES
dc.relation.ispartof Journal of Computational and Applied Mathematics es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Nonlinear systems es_ES
dc.subject Iterative method es_ES
dc.subject Convergence es_ES
dc.subject Efficiency index es_ES
dc.subject Fisher's equation es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p>5 es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cam.2017.02.032 es_ES
dc.rights.accessRights Embargado es_ES
dc.date.embargoEndDate 2020-03-01 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.; Jordan-Lluch, C.; Sanabria-Codesal, E.; Torregrosa Sánchez, JR. (2018). Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p>5. Journal of Computational and Applied Mathematics. 330:748-758. https://doi.org/10.1016/j.cam.2017.02.032 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.cam.2017.02.032 es_ES
dc.description.upvformatpinicio 748 es_ES
dc.description.upvformatpfin 758 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 330 es_ES
dc.relation.pasarela 348001 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES


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