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Solving a reaction-diffusion system with chemotaxis and non-local terms using Generalized Finite Difference Method. Study of the convergence

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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, M. A.
dc.date.accessioned2023-06-17T08:57:49Z
dc.date.available2023-06-17T08:57:49Z
dc.date.issued2021-06
dc.description.abstractIn this paper a parabolic-parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the two dimensional case. Several examples of the application are given to illustrate the accuracy and efficiency of the numerical method. We also present two examples of a parabolic-elliptic model, as generalized by the parabolic-parabolic system addressed in this paper, to show the validity of the discretization of the non-local terms.
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.sponsorshipUniversidad Nacional de Educación a Distancia (UNED)
dc.description.sponsorshipUniversidad Politécnica de Madrid (UPM)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/63721
dc.identifier.doi10.1016/j.cam.2020.113325
dc.identifier.issn0377-0427
dc.identifier.officialurlhttp://www.journals.elsevier.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7734
dc.journal.titleJournal of Computational and Applied Mathematics
dc.language.isoeng
dc.page.initial113325
dc.publisherElsevier
dc.relation.projectIDMTM2017-42907-P
dc.relation.projectID2019-IFC02
dc.relation.projectID(Research groups 2019)
dc.rights.accessRightsopen access
dc.subject.cdu517.98
dc.subject.cdu519.6
dc.subject.keywordChemotaxis system
dc.subject.keywordGeneralized Finite Difference
dc.subject.keywordMeshless method
dc.subject.keywordAsymptotic stability
dc.subject.keywordQuimiotaxis
dc.subject.keywordEstabilidad asintótica
dc.subject.keywordMétodos sin malla
dc.subject.keywordDiferencias finitas generalizadas
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.subject.ucmAnálisis numérico
dc.subject.unesco12 Matemáticas
dc.subject.unesco1206 Análisis Numérico
dc.titleSolving a reaction-diffusion system with chemotaxis and non-local terms using Generalized Finite Difference Method. Study of the convergence
dc.typejournal article
dc.volume.number389
dcterms.references[1] Anderson A.R., Chaplain M.A., Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol., 60 (5), 857–899,(1998). [2] Benito J. J., Garcia A., Gavete L., Negreanu M., Ure˜na F., Vargas A. M., On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences. Engineering Analysis with Boundary Elements, 113C, 181–190 (2020). [3] Ding M., Wang W., Zhou S., Zheng S., Asymptotic stability in a fully parabolic quasilinear chemotaxis model with general logistic source and signal production. Journal of Differential Equations (2019), https://doi.org/10.1016/j.jde.2019.11.052. [4] Horstmann D., From 1970 until present: the Keller-Segel model in chemotaxis and its consequences, Jahresbericht der Deutschen Mathematiker-Vereinigung. 105 (3), (2003), 103–165. [5] Keller EF., Segel LA. Initiation of slime mold aggregation viewed as an instability. J. Theoret. Biol. 26, 399-415, (1970). [6] Negreanu M., Tello J.I., On a competitive system under chemotactic effects with non-local terms. Nonlinearity, 26 (4), 1083–1103 (2013). [7] Negreanu M., Tello J.I., Vargas A.M. (2017), On a Parabolic-Elliptic chemotaxis system with periodic asymptotic behavior, Mathematical Methods in Applied Sciences, https://doi.org/10.1002/mma.5423. [8] Negreanu M., Tello J.I., Vargas A.M. (2020), On a fully Parabolic chemotaxis system with source term and periodic asymptotic behavior, to appear in Zeitschrift für angewandte Mathematik und Physik. [9] Szymanska Z., Morales Rodrigo C., Lachowicz M., Chaplain M.A.J., Mathematical modelling of cancer invasion of tissue the role and effect of nonlocal interactions. Mathematical Models and Methods in Applied Sciences, 19 (2), 257-281 (2009). [10] Ureña F., Gavete L., Benito J.J., Garc´ıa A., Vargas A.M., Solving the telegraph equation in 2-D and 3-D using generalized finite difference method (GFDM). Engineering Analysis with Boundary Elements, 112, 13–24, (2020). [11] Ureña F., Gavete L., Garcia A., Benito J. J., Vargas A. M., Solving second order non-linear parabolic PDEs using generalized finite difference method (GFDM), Journal of Computational and Applied Mathematics, 354, (2019), 221–241.
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relation.isAuthorOfPublication.latestForDiscovery34eacc25-4f35-4e28-9665-9a3764841087

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