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Symplectic integrators for the matrix Hill equation

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Symplectic integrators for the matrix Hill equation

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dc.contributor.author Bader, Philipp es_ES
dc.contributor.author Blanes Zamora, Sergio es_ES
dc.contributor.author Ponsoda Miralles, Enrique es_ES
dc.contributor.author Seydaoglu, Muaz es_ES
dc.date.accessioned 2018-11-14T21:01:57Z
dc.date.available 2018-11-14T21:01:57Z
dc.date.issued 2017 es_ES
dc.identifier.issn 0377-0427 es_ES
dc.identifier.uri http://hdl.handle.net/10251/112490
dc.description.abstract [EN] We consider the numerical integration of the matrix Hill equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, Hill s equations originate from a Hamiltonian function and the fundamental matrix solution is a symplectic matrix. This is a very important property to be preserved by the numerical integrators. In this work we present new sixth-and eighth-order symplectic exponential integrators that are tailored to Hill s equation. The methods are based on an efficient symplectic approximation to the exponential of high dimensional coupled autonomous harmonic oscillators and yield accurate results for oscillatory problems at a low computational cost. The proposed methods can also be used for solving general second order linear differential equations where their performance will depend on how the methods are finally adapted to each particular problem or the qualitative properties one is interested to preserve. Several numerical examples illustrate the performance of the new methods. es_ES
dc.description.sponsorship The authors thank the anonymous referees for criticism and comments which helped to clarify the present paper. PB and SB acknowledge the Ministerio de Economia y Competitividad (Spain) for financial support through the coordinated project MTM2013-46553-C3.
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation info:eu-repo/grantAgreement/MINECO//MTM2013-46553-C3-3-P/ES/METODOS DE ESCISION Y COMPOSICION EN INTEGRACION NUMERICA GEOMETRICA. TEORIA Y APLICACIONES/ es_ES
dc.relation.ispartof Journal of Computational and Applied Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Matrix Hill equation es_ES
dc.subject Mathieu equation es_ES
dc.subject Parametric resonance es_ES
dc.subject Symplectic integrators es_ES
dc.subject Magnus expansion es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Symplectic integrators for the matrix Hill equation es_ES
dc.type Artículo es_ES
dc.type Comunicación en congreso es_ES
dc.identifier.doi 10.1016/j.cam.2016.09.041 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 Bader, P.; Blanes Zamora, S.; Ponsoda Miralles, E.; Seydaoglu, M. (2017). Symplectic integrators for the matrix Hill equation. Journal of Computational and Applied Mathematics. 316:47-59. https://doi.org/10.1016/j.cam.2016.09.041 es_ES
dc.description.accrualMethod S es_ES
dc.relation.conferencename 14th Seminar on the Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-14) es_ES
dc.relation.conferencedate Septiembre 07-11,2015 es_ES
dc.relation.conferenceplace Halle, Germany es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.cam.2016.09.041 es_ES
dc.description.upvformatpinicio 47 es_ES
dc.description.upvformatpfin 59 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 316 es_ES
dc.relation.pasarela S\325881 es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES


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