Una introducción al uso de las funciones de base radial para resolver numéricamente ecuaciones diferenciales parciales

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dc.contributor.advisorVillamizar Roa, Elder Jesús
dc.contributor.advisorSánchez Galvis, Iván Javier
dc.contributor.authorChávez Sánchez, Danna Katherine
dc.date.accessioned2024-03-04T01:15:08Z
dc.date.available2021
dc.date.available2024-03-04T01:15:08Z
dc.date.created2021
dc.date.issued2021
dc.description.abstractEste trabajo está relacionado con el análisis numérico de soluciones de ecuaciones diferenciales parciales mediante funciones de base radial. Este trabajo consta de tres partes fundamentales; el primerocorresponde a una revisión de definiciones y resultados preliminares sobre la interpolación con
dc.description.abstractenglishThis work is related to the numerical analysis of solutions of partial differential equations through radialbasis functions. This work consists of three fundamental parts; the first one corresponds to a review ofdefinitions and preliminaries results on the interpolation with radial basis functions, the defined positivefunctions and conditionally defined functions, as well as some of their characterizations. From the generalization of the mentioned functions, we study the associated function space, denominated «Nativespace», which is required to establish the convergence of the interpolator. The second part is devoted to the description of the Asymmetric Collocation Method for a general linear problem. This methodwas proposed by E. J. Kansa in 199qiP which has been used in the approximation of solutions forpartial differential equations by means of radial basis functions. Moreover, the order of exponential convergence of the asymmetric collocation method is verified using the multi-quadratic radial function in atwo-dimensional Poisson problem with mixed boundary conditions. Finally, in the third part, the Asymmetric Collocation Method is analyzed for the linear heat equation in the bi-dimensional setting, basedon the multi-quadratic radial function, and with an implicit and explicit scheme in the temporal discretization. Besides, in both parts of the numerical implementation using the Asymmetric Collocation Method,a comparison between the mesh-free method and the classical method finite elements is carried out.
dc.description.degreelevelPregrado
dc.description.degreenameMatemático
dc.format.mimetypeapplication/pdf
dc.identifier.instnameUniversidad Industrial de Santander
dc.identifier.reponameUniversidad Industrial de Santander
dc.identifier.repourlhttps://noesis.uis.edu.co
dc.identifier.urihttps://noesis.uis.edu.co/handle/20.500.14071/41309
dc.language.isospa
dc.publisherUniversidad Industrial de Santander
dc.publisher.facultyFacultad de Ciencias
dc.publisher.programMatemáticas
dc.publisher.schoolEscuela de Matemáticas
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.rights.creativecommonsAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
dc.rights.licenseAttribution-NonCommercial 4.0 International (CC BY-NC 4.0)
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0
dc.subjectMétodos Libres De Malla
dc.subjectInterpolación Con Funciones De Baseradial
dc.subjectMétodo De Colocación Asimétrico
dc.subjectConvergencia Exponencial
dc.subjectFunción radial Multicuadrática
dc.subjectMétodo De Elementos Finitos.
dc.subject.keywordMesh-Free Method
dc.subject.keywordInterpolation With Radial Basis Functions
dc.subject.keywordAsymmetric Collocation Method
dc.subject.keywordExponential Convergence
dc.subject.keywordMultiquadratic Radialfunction
dc.subject.keywordFinite Elementes Method.
dc.titleUna introducción al uso de las funciones de base radial para resolver numéricamente ecuaciones diferenciales parciales
dc.title.englishAn introduction to the use of radial basis functions for the numericalsolution of partial differential equations. []
dc.type.coarhttp://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.hasversionhttp://purl.org/coar/resource_type/c_7a1f
dc.type.localTesis/Trabajo de grado - Monografía - Pregrado
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