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Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs

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Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs

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dc.contributor.author Blanes Zamora, Sergio es_ES
dc.contributor.author Ponsoda Miralles, Enrique es_ES
dc.date.accessioned 2015-10-19T11:32:32Z
dc.date.available 2015-10-19T11:32:32Z
dc.date.issued 2012-08
dc.identifier.issn 0168-9274
dc.identifier.uri http://hdl.handle.net/10251/56205
dc.description.abstract We consider time-averaging methods based on the Magnus series expansion jointly with exponential integrators for the numerical integration of general linear non-homogeneous differential equations. The schemes can be considered as averaged methods which transform, for one time step, a non-autonomous problem into an autonomous one whose flows agree up to a given order of accuracy at the end of the time step. The problem is reformulated as a particular case of a matrix Riccati differential equation and the Möbius transformation is considered, leading to a homogeneous linear problem. The methods proposed can be used both for initial value problems (IVPs) as well as for two-point boundary value problems (BVPs). In addition, they allow to use different approximations for different parts of the equation, e.g. the homogeneous and non-homogeneous parts, or to use adaptive time steps. The particular case of separated boundary conditions using the imbedding formulation is also considered. This formulation allows us to transform a stiff and badly conditioned BVP into a set of well conditioned IVPs which can be integrated using some of the previous methods. The performance of the methods is illustrated on some numerical examples. © 2012 IMACS. Published by Elsevier B.V. All rights reserved. es_ES
dc.description.sponsorship We would like to thank the referees for their suggestions and comments that helped us to improve the presentation of the work as well as to clarify the main results. The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032. The work of S.B. has also been partially supported by Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03 (co-financed by the ERDF of the European Union) and the work of E.P. has also been partially supported by Ministerio de Ciencia e Innvacion of Spain, by the project MTM2009-08587. en_EN
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Applied Numerical Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Exponential integrators es_ES
dc.subject Imbedding formulation es_ES
dc.subject Linear initial and boundary value problem es_ES
dc.subject Matrix Riccati differential equation es_ES
dc.subject Adaptive time step es_ES
dc.subject Linear problems es_ES
dc.subject Non-homogeneous es_ES
dc.subject Nonautonomous es_ES
dc.subject Numerical example es_ES
dc.subject Numerical integrations es_ES
dc.subject Order of accuracy es_ES
dc.subject Series expansion es_ES
dc.subject Time averaging es_ES
dc.subject Time step es_ES
dc.subject Two-point boundary value problem es_ES
dc.subject Boundary conditions es_ES
dc.subject Initial value problems es_ES
dc.subject Linear transformations es_ES
dc.subject Mathematical transformations es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.apnum.2012.02.001
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2009-08587/ES/Ecuaciones Diferenciales Aleatorias Y Aplicaciones/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2010-18246-C03-01/ES/RETOS EN INTEGRACION NUMERICA: GEOMETRIA, OSCILACIONES Y PROCESOS ESTOCASTICOS/
dc.relation.projectID info:eu-repo/grantAgreement/Generalitat Valenciana//GV%2F2009%2F032/ES/Desarrollo de integradores geométricos adaptados a ecuaciones diferenciales con diferentes escalas de tiempo/
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 Blanes Zamora, S.; Ponsoda Miralles, E. (2012). Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs. Applied Numerical Mathematics. 62(8):875-894. doi:10.1016/j.apnum.2012.02.001 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.apnum.2012.02.001 es_ES
dc.description.upvformatpinicio 875 es_ES
dc.description.upvformatpfin 894 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 62 es_ES
dc.description.issue 8 es_ES
dc.relation.senia 231621 es_ES
dc.contributor.funder Generalitat Valenciana
dc.contributor.funder Ministerio de Ciencia e Innovación


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