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dc.contributor.author | Blanes Zamora, Sergio | es_ES |
dc.date.accessioned | 2019-05-31T20:43:14Z | |
dc.date.available | 2019-05-31T20:43:14Z | |
dc.date.issued | 2018 | es_ES |
dc.identifier.issn | 0036-1429 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/121360 | |
dc.description.abstract | [EN] In this work we show how to numerically integrate nonautonomous differential equations by solving alternate time-averaged differential equations. Given a quadrature rule of order 2s or higher for s = 1, 2, . . . , we show how to build a differential equation with an averaged vector field that is a polynomial function of degree s - 1 in the independent variable, t, and whose solution after one time step agrees with the solution of the original differential equation up to order 2s. Then, any numerical scheme can be used to solve this alternate averaged equation where the vector field is always evaluated at the chosen quadrature rule. We show how to use the Magnus series expansion, adapted to nonlinear problems, to build the formal solution, and this result is valid for any choice of the quadrature rule. This formal solution can be used to build new schemes that must agree with it up to the desired order. For example, we show how to build commutator-free methods from previous results in the literature. All methods can also be written in terms of moment integrals, and each integral can be computed using different quadrature rules. This procedure allows us to build tailored methods for different classes of problems. We illustrate the time-averaged procedure and its efficiency in solving several problems. | es_ES |
dc.description.sponsorship | This work was funded by Ministerio de Economia, Industria y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE). | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Society for Industrial and Applied Mathematics | es_ES |
dc.relation.ispartof | SIAM Journal on Numerical Analysis | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Nonautonomous differential equations | es_ES |
dc.subject | Time-averaged differential equations | es_ES |
dc.subject | Quadrature rules | es_ES |
dc.subject | Geometric integration | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Time-average on the numerical integration of nonautonomous differential equations | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1137/17M1156150 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2016-77660-P/ES/NUEVOS RETOS EN INTEGRACION NUMERICA: FUNDAMENTOS ALGEBRAICOS, METODOS DE ESCISION, METODOS DE MONTECARLO Y OTRAS 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 | Blanes Zamora, S. (2018). Time-average on the numerical integration of nonautonomous differential equations. SIAM Journal on Numerical Analysis. 56(4):2513-2536. https://doi.org/10.1137/17M1156150 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | http://doi.org/10.1137/17M1156150 | es_ES |
dc.description.upvformatpinicio | 2513 | es_ES |
dc.description.upvformatpfin | 2536 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 56 | es_ES |
dc.description.issue | 4 | es_ES |
dc.relation.pasarela | S\380522 | es_ES |
dc.contributor.funder | Ministerio de Economía y Competitividad | es_ES |