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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/150454
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/150454
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-10-22T12:06:10Zoai: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:34982025-10-22 12:06:10.597CONICET 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
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv 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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score 12.982451

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