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Complex Ginzburg–Landau equation with generalized finite differences

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dc.contributor.authorSalete, Eduardo
dc.contributor.authorVargas, A. M.
dc.contributor.authorGarcía, Ángel
dc.contributor.authorNegreanu Pruna, Mihaela
dc.contributor.authorBenito, Juan J.
dc.contributor.authorUreña, Francisco
dc.date.accessioned2023-06-17T08:57:44Z
dc.date.available2023-06-17T08:57:44Z
dc.date.issued2020-12-20
dc.description.abstractIn this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equation into a system of two parabolic PDEs. We prove the conditional convergence of the numerical scheme towards the continuous solution under certain assumptions. We obtain a second order approximation as it is clear from the numerical results. Finally, we provide several examples of its application over irregular domains in order to test the accuracy of the explicit scheme, as well as comparison with other numerical methods.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.sponsorshipEscuela Técnica Superior de Ingenieros Industriales (UNED)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/63706
dc.identifier.doi10.3390/math8122248
dc.identifier.issn2227-7390
dc.identifier.officialurlhttps://doi.org/10.3390/math8122248
dc.identifier.relatedurlhttps://www.mdpi.com/2227-7390/8/12/2248
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7727
dc.issue.number12
dc.journal.titleMathematics
dc.language.isoeng
dc.page.initial2248
dc.publisherMDPI
dc.relation.projectIDMTM2017-83391-P
dc.relation.projectID2020-IFC02
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu517
dc.subject.keywordGinzburg–Landau equation
dc.subject.keywordparabolic-parabolic systems
dc.subject.keywordgeneralized finite difference method
dc.subject.keywordEcuación de Ginzburg-Landau
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmAnálisis matemático
dc.subject.unesco12 Matemáticas
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleComplex Ginzburg–Landau equation with generalized finite differences
dc.typejournal article
dc.volume.number8
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