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On the convergence of the Generalized Finite Difference Method for solving a chemotaxis system with no chemical diffusion

dc.contributor.authorBenito, J. J.
dc.contributor.authorGarcía, A.
dc.contributor.authorGavete, L.
dc.contributor.authorNegreanu Pruna, Mihaela
dc.contributor.authorUreña, F.
dc.contributor.authorVargas, A. M.
dc.date.accessioned2023-06-17T08:29:37Z
dc.date.available2023-06-17T08:29:37Z
dc.date.issued2021
dc.description.abstractThis paper focuses on the numerical analysis of a discrete version of a nonlinear reaction–diffusion system consisting of an ordinary equation coupled to a quasilinear parabolic PDE with a chemotactic term. The parabolic equation of the system describes the behavior of a biological species, while the ordinary equation defines the concentration of a chemical substance. The system also includes a logistic-like source, which limits the growth of the biological species and presents a time-periodic asymptotic behavior. We study the convergence of the explicit discrete scheme obtained by means of the generalized finite difference method and prove that the nonnegative numerical solutions in two-dimensional space preserve the asymptotic behavior of the continuous ones. Using different functions and long-time simulations, we illustrate the efficiency of the developed numerical algorithms in the sense of the convergence in space and in time.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/74749
dc.identifier.doi10.1007/s40571-020-00359-w
dc.identifier.issn2196-4378
dc.identifier.officialurlhttps://doi.org/10.1007/s40571-020-00359-w
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7281
dc.journal.titleComputational Particle Mechanics
dc.language.isoeng
dc.page.final636
dc.page.initial625
dc.publisherSpringer
dc.rights.accessRightsopen access
dc.subject.cdu519.6
dc.subject.keywordChemotaxis systems
dc.subject.keywordGeneralized Finite difference
dc.subject.keywordMeshless method
dc.subject.keywordAsymptotic stability
dc.subject.ucmAnálisis numérico
dc.subject.unesco1206 Análisis Numérico
dc.titleOn the convergence of the Generalized Finite Difference Method for solving a chemotaxis system with no chemical diffusion
dc.typejournal article
dc.volume.number8
dspace.entity.typePublication
relation.isAuthorOfPublication34eacc25-4f35-4e28-9665-9a3764841087
relation.isAuthorOfPublication.latestForDiscovery34eacc25-4f35-4e28-9665-9a3764841087

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