Publication:
Solving Non-Smooth Delay Differential Equations with Multiquadrics

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorBernal Martínez, Francisco Manuel
dc.date.accessioned2021-03-08T11:30:40Z
dc.date.available2021-03-08T11:30:40Z
dc.date.issued2012-01-14
dc.descriptionProceeding of: 16th Conference of the European Consortium for Mathematics in Industry (ECMI 2010), Wuppertal, Germany, Wuppertal, from July 26 to July 30, 2010.en
dc.description.abstractWe put forward a discretization scheme for the numerical solution of neutral differential equations (NDEs). The solution to the NDE in an interval I = [a, b] is approximated by a multiquadric (MQ) interpolant, whose coefficients are found by collocation on a set of N nodes in I. This approach, also known as Kansa’s method, enjoys an exponential rate of convergence and great flexibility regarding the location of the nodes, as long as the solution to the differential equation is smooth. However, the critical difficulty posed by NDEs is precisely that they propagate, forward in time and without damping, low-order discontinuities of the history function. Here, we exploit the sensitivity of the MQ interpolant to discontinuities in order to detect them in computing time. This allows for a partition of I into smooth subintervals, which are then sequentially solved by Kansa’s method.en
dc.description.statusPublicadoes
dc.format.extent6
dc.identifier.bibliographicCitationGünther M., Bartel A., Brunk M., Schöps S., Striebel M. (eds). (2012) Progress in Industrial Mathematics at ECMI 2010. (Mathematics in Industry. TECMI; 17). Springer-Verlag Berlin Heidelberg. Pp. 603-609.en
dc.identifier.doihttps://doi.org/10.1007/978-3-642-25100-9_70
dc.identifier.isbn978-3-642-25099-6 (print)
dc.identifier.issn978-3-642-25100-9 (online)
dc.identifier.publicationfirstpage603
dc.identifier.publicationlastpage609
dc.identifier.publicationtitleProgress in Industrial Mathematics at ECMI 2010en
dc.identifier.publicationvolume17
dc.identifier.urihttps://hdl.handle.net/10016/32079
dc.identifier.uxxiCO/0000010856
dc.language.isoengen
dc.publisherSpringer Verlag Berlin-Heidelbergen
dc.relation.eventdateJuly 26 to July 30, 2010en
dc.relation.eventnumber16
dc.relation.eventplaceWuppertal, Alemania
dc.relation.eventtitleConference of the European Consortium for Mathematics in Industry (ECMI 2010)en
dc.relation.ispartofseriesMathematics in Industry (MATHINDUSTRY); 17en
dc.relation.ispartofseriesThe European Consortium for Mathematics in Industry (TECMI); 17en
dc.rights© Springer-Verlag Berlin Heidelberg 2012en
dc.rights.accessRightsopen accessen
dc.subject.ecienciaIngeniería Industriales
dc.subject.ecienciaMatemáticases
dc.subject.otherDelay differential equationen
dc.subject.otherJump discontinuityen
dc.subject.otherHistory functionen
dc.subject.otherGibbs phenomenonen
dc.subject.otherNeutral differential equationen
dc.titleSolving Non-Smooth Delay Differential Equations with Multiquadricsen
dc.typeconference paper*
dc.type.hasVersionAM*
dc.type.reviewPeerRevieweden
dspace.entity.typePublication
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