Finite difference schemes for a structured population model in the space of measures
- Autores
- Ackleh, Azmy S.; Lyons, Rainey; Saintier, Nicolas Bernard Claude
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We present two finite-difference methods for approximating solutions to a structured population model in the space of non-negative Radon Measures. The first method is a first-order upwind-based scheme and the second is high-resolution method of second-order. We prove that the two schemes converge to the solution in the Bounded-Lipschitz norm. Several numerical examples demonstrating the order of convergence and behavior of the schemes around singularities are provided. In particular, these numerical results show that for smooth solutions the upwind and high-resolution methods provide a first-order and a second-order approximation, respectively. Furthermore, for singular solutions the second-order high-resolution method is superior to the first-order method.
Fil: Ackleh, Azmy S.. State University of Louisiana; Estados Unidos
Fil: Lyons, Rainey. State University of Louisiana; Estados Unidos
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina - Materia
-
BOUNDED-LIPSCHITZ NORM
FINITE DIFFERENCE SCHEMES
HIGH-RESOLUTION METHODS
NON-NEGATIVE RADON MEASURES
STRUCTURED POPULATIONS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/150454
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Finite difference schemes for a structured population model in the space of measuresAckleh, Azmy S.Lyons, RaineySaintier, Nicolas Bernard ClaudeBOUNDED-LIPSCHITZ NORMFINITE DIFFERENCE SCHEMESHIGH-RESOLUTION METHODSNON-NEGATIVE RADON MEASURESSTRUCTURED POPULATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present two finite-difference methods for approximating solutions to a structured population model in the space of non-negative Radon Measures. The first method is a first-order upwind-based scheme and the second is high-resolution method of second-order. We prove that the two schemes converge to the solution in the Bounded-Lipschitz norm. Several numerical examples demonstrating the order of convergence and behavior of the schemes around singularities are provided. In particular, these numerical results show that for smooth solutions the upwind and high-resolution methods provide a first-order and a second-order approximation, respectively. Furthermore, for singular solutions the second-order high-resolution method is superior to the first-order method.Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Lyons, Rainey. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Institute of Mathematical Sciences2020-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150454Ackleh, Azmy S.; Lyons, Rainey; Saintier, Nicolas Bernard Claude; Finite difference schemes for a structured population model in the space of measures; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 17; 1; 1-2020; 747-7751547-1063CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.aimspress.com/fileOther/PDF/MBE/mbe-17-01-039.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.3934/mbe.2020039info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:33:38Zoai:ri.conicet.gov.ar:11336/150454instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:33:38.666CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Finite difference schemes for a structured population model in the space of measures |
title |
Finite difference schemes for a structured population model in the space of measures |
spellingShingle |
Finite difference schemes for a structured population model in the space of measures Ackleh, Azmy S. BOUNDED-LIPSCHITZ NORM FINITE DIFFERENCE SCHEMES HIGH-RESOLUTION METHODS NON-NEGATIVE RADON MEASURES STRUCTURED POPULATIONS |
title_short |
Finite difference schemes for a structured population model in the space of measures |
title_full |
Finite difference schemes for a structured population model in the space of measures |
title_fullStr |
Finite difference schemes for a structured population model in the space of measures |
title_full_unstemmed |
Finite difference schemes for a structured population model in the space of measures |
title_sort |
Finite difference schemes for a structured population model in the space of measures |
dc.creator.none.fl_str_mv |
Ackleh, Azmy S. Lyons, Rainey Saintier, Nicolas Bernard Claude |
author |
Ackleh, Azmy S. |
author_facet |
Ackleh, Azmy S. Lyons, Rainey Saintier, Nicolas Bernard Claude |
author_role |
author |
author2 |
Lyons, Rainey Saintier, Nicolas Bernard Claude |
author2_role |
author author |
dc.subject.none.fl_str_mv |
BOUNDED-LIPSCHITZ NORM FINITE DIFFERENCE SCHEMES HIGH-RESOLUTION METHODS NON-NEGATIVE RADON MEASURES STRUCTURED POPULATIONS |
topic |
BOUNDED-LIPSCHITZ NORM FINITE DIFFERENCE SCHEMES HIGH-RESOLUTION METHODS NON-NEGATIVE RADON MEASURES STRUCTURED POPULATIONS |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
We present two finite-difference methods for approximating solutions to a structured population model in the space of non-negative Radon Measures. The first method is a first-order upwind-based scheme and the second is high-resolution method of second-order. We prove that the two schemes converge to the solution in the Bounded-Lipschitz norm. Several numerical examples demonstrating the order of convergence and behavior of the schemes around singularities are provided. In particular, these numerical results show that for smooth solutions the upwind and high-resolution methods provide a first-order and a second-order approximation, respectively. Furthermore, for singular solutions the second-order high-resolution method is superior to the first-order method. Fil: Ackleh, Azmy S.. State University of Louisiana; Estados Unidos Fil: Lyons, Rainey. State University of Louisiana; Estados Unidos Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina |
description |
We present two finite-difference methods for approximating solutions to a structured population model in the space of non-negative Radon Measures. The first method is a first-order upwind-based scheme and the second is high-resolution method of second-order. We prove that the two schemes converge to the solution in the Bounded-Lipschitz norm. Several numerical examples demonstrating the order of convergence and behavior of the schemes around singularities are provided. In particular, these numerical results show that for smooth solutions the upwind and high-resolution methods provide a first-order and a second-order approximation, respectively. Furthermore, for singular solutions the second-order high-resolution method is superior to the first-order method. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/150454 Ackleh, Azmy S.; Lyons, Rainey; Saintier, Nicolas Bernard Claude; Finite difference schemes for a structured population model in the space of measures; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 17; 1; 1-2020; 747-775 1547-1063 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/150454 |
identifier_str_mv |
Ackleh, Azmy S.; Lyons, Rainey; Saintier, Nicolas Bernard Claude; Finite difference schemes for a structured population model in the space of measures; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 17; 1; 1-2020; 747-775 1547-1063 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.aimspress.com/fileOther/PDF/MBE/mbe-17-01-039.pdf info:eu-repo/semantics/altIdentifier/doi/10.3934/mbe.2020039 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
American Institute of Mathematical Sciences |
publisher.none.fl_str_mv |
American Institute of Mathematical Sciences |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.070432 |