Solution of a time fractional inverse advection-dispersion problem by discrete mollification
ABSTRACT: We consider an inverse problem for a time fractional advection-dispersion equation in a 1-D semi-infinite setting. The fractional derivative is interpreted in the sense of Caputo and advection and dispersion coefficients are constant. The inverse problem consists on the recovery of the bou...
- Autores:
-
Mejía, Carlos
Piedrahita Monroy, Julian Alejandro
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2017
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/29203
- Acceso en línea:
- http://hdl.handle.net/10495/29203
http://www.scielo.org.co/scielo.php?pid=S0034-74262017000100083&script=sci_abstract&tlng=en
- Palabra clave:
- Derivadas (Matemáticas)
Diferencias finitas
Finite Differences
Derivadas fraccionales
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
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| dc.title.spa.fl_str_mv |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| dc.title.alternative.spa.fl_str_mv |
Solución de un problema inverso de advección-dispersión con derivada temporal fraccionaria por medio de molificación discreta |
| title |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| spellingShingle |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification Derivadas (Matemáticas) Diferencias finitas Finite Differences Derivadas fraccionales |
| title_short |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| title_full |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| title_fullStr |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| title_full_unstemmed |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| title_sort |
Solution of a time fractional inverse advection-dispersion problem by discrete mollification |
| dc.creator.fl_str_mv |
Mejía, Carlos Piedrahita Monroy, Julian Alejandro |
| dc.contributor.author.none.fl_str_mv |
Mejía, Carlos Piedrahita Monroy, Julian Alejandro |
| dc.subject.lemb.none.fl_str_mv |
Derivadas (Matemáticas) Diferencias finitas Finite Differences |
| topic |
Derivadas (Matemáticas) Diferencias finitas Finite Differences Derivadas fraccionales |
| dc.subject.proposal.spa.fl_str_mv |
Derivadas fraccionales |
| description |
ABSTRACT: We consider an inverse problem for a time fractional advection-dispersion equation in a 1-D semi-infinite setting. The fractional derivative is interpreted in the sense of Caputo and advection and dispersion coefficients are constant. The inverse problem consists on the recovery of the boundary distribution of solute concentration and dispersion flux from measured (noisy) data known at an interior location. This inverse problem is ill-posed and thus the numerical solution must include some regularization technique. Our approach is a finite difference space marching scheme enhanced by adaptive discrete mollification. Error estimates and illustrative numerical examples are provided. |
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2017 |
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2017 |
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2022-06-14T17:57:08Z |
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2022-06-14T17:57:08Z |
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Artículo de investigación |
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Mejía, Carlos, & Piedrahita H, Alejandro. (2017). Solution of a time fractional inverse advection-dispersion problem by discrete mollification. Revista Colombiana de Matemáticas, 51(1), 83-102. https://doi.org/10.15446/recolma.v51n1.66839 |
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0034-7426 |
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http://hdl.handle.net/10495/29203 |
| dc.identifier.doi.none.fl_str_mv |
10.15446/recolma.v51n1.66839. |
| dc.identifier.eissn.none.fl_str_mv |
2357-4100 |
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http://www.scielo.org.co/scielo.php?pid=S0034-74262017000100083&script=sci_abstract&tlng=en |
| identifier_str_mv |
Mejía, Carlos, & Piedrahita H, Alejandro. (2017). Solution of a time fractional inverse advection-dispersion problem by discrete mollification. Revista Colombiana de Matemáticas, 51(1), 83-102. https://doi.org/10.15446/recolma.v51n1.66839 0034-7426 10.15446/recolma.v51n1.66839. 2357-4100 |
| url |
http://hdl.handle.net/10495/29203 http://www.scielo.org.co/scielo.php?pid=S0034-74262017000100083&script=sci_abstract&tlng=en |
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eng |
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eng |
| dc.relation.ispartofjournalabbrev.spa.fl_str_mv |
Rev. Colomb. Mat. |
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info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by/2.5/co/ |
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openAccess |
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Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Matemáticas |
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EMAC - Enseñanza de Matemáticas y Computación |
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Bogotá, Colombia |
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Universidad de Antioquia |
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Mejía, CarlosPiedrahita Monroy, Julian Alejandro2022-06-14T17:57:08Z2022-06-14T17:57:08Z2017Mejía, Carlos, & Piedrahita H, Alejandro. (2017). Solution of a time fractional inverse advection-dispersion problem by discrete mollification. Revista Colombiana de Matemáticas, 51(1), 83-102. https://doi.org/10.15446/recolma.v51n1.668390034-7426http://hdl.handle.net/10495/2920310.15446/recolma.v51n1.66839.2357-4100http://www.scielo.org.co/scielo.php?pid=S0034-74262017000100083&script=sci_abstract&tlng=enABSTRACT: We consider an inverse problem for a time fractional advection-dispersion equation in a 1-D semi-infinite setting. The fractional derivative is interpreted in the sense of Caputo and advection and dispersion coefficients are constant. The inverse problem consists on the recovery of the boundary distribution of solute concentration and dispersion flux from measured (noisy) data known at an interior location. This inverse problem is ill-posed and thus the numerical solution must include some regularization technique. Our approach is a finite difference space marching scheme enhanced by adaptive discrete mollification. Error estimates and illustrative numerical examples are provided.RESUMEN: Consideramos un problema inverso para una ecuación de advección-dispersión con derivada temporal fraccionaria, en una configuración unidimensional. La derivada fraccionaria se interpreta en el sentido de Caputo y las coeficientes de advección y de dispersión son constantes. El problema inverso involucra la reconstrucción simultánea de la concentración de soluto y del flujo de dispersión en una de las fronteras del dominio físico, a partir de lecturas de datos perturbados en un punto interior del dominio. Mostramos que el problema inverso es mal condicionado y por tanto una solución numérica del problema requiere de alguna técnica de regularización. Proponemos un esquema de diferencias finitas de marcha en el espacio, que utiliza molificación discreta como técnica de regularización. Se incluyen estimativos de error y ejemplos numéricos ilustrativos.COL018055720application/pdfengUniversidad Nacional de Colombia, Facultad de Ciencias, Departamento de MatemáticasEMAC - Enseñanza de Matemáticas y ComputaciónBogotá, Colombiainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Solution of a time fractional inverse advection-dispersion problem by discrete mollificationSolución de un problema inverso de advección-dispersión con derivada temporal fraccionaria por medio de molificación discretaDerivadas (Matemáticas)Diferencias finitasFinite DifferencesDerivadas fraccionalesRev. Colomb. Mat.Revista Colombiana de Matemáticas83102511CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927https://bibliotecadigital.udea.edu.co/bitstream/10495/29203/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/29203/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD53ORIGINALPidrahitaAlejandro_2017_SolutionTimeFractional.pdfPidrahitaAlejandro_2017_SolutionTimeFractional.pdfArtículo de investigaciónapplication/pdf682511https://bibliotecadigital.udea.edu.co/bitstream/10495/29203/1/PidrahitaAlejandro_2017_SolutionTimeFractional.pdff4083f286fa73bb0edad5f087f9ec5afMD5110495/29203oai:bibliotecadigital.udea.edu.co:10495/292032022-06-14 12:57:09.099Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |