Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption

Autores
Dratman, Ezequiel
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is small enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an ε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Two-Point Boundary-Value Problem
Stationary Solution
Homotopy Continuation
Complexity
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:11336/24826
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/24826
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorptionDratman, EzequielTwo-Point Boundary-Value ProblemStationary SolutionHomotopy ContinuationComplexityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is small enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an ε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier2013-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/24826Dratman, Ezequiel; Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption; Elsevier; Journal Of Complexity; 29; 3-4; 3-2013; 263-2820885-064XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0885064X13000186info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2013.03.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:56:42Zoai:ri.conicet.gov.ar:11336/24826instacron: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 09:56:42.779CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
title Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
spellingShingle Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
Dratman, Ezequiel
Two-Point Boundary-Value Problem
Stationary Solution
Homotopy Continuation
Complexity
title_short Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
title_full Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
title_fullStr Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
title_full_unstemmed Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
title_sort Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption
dc.creator.none.fl_str_mv Dratman, Ezequiel
author Dratman, Ezequiel
author_facet Dratman, Ezequiel
author_role author
dc.subject.none.fl_str_mv Two-Point Boundary-Value Problem
Stationary Solution
Homotopy Continuation
Complexity
topic Two-Point Boundary-Value Problem
Stationary Solution
Homotopy Continuation
Complexity
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 study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is small enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an ε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is small enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the “continuous” equation. Furthermore, we exhibit an algorithm computing an ε-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
publishDate 2013
dc.date.none.fl_str_mv 2013-03
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/11336/24826
Dratman, Ezequiel; Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption; Elsevier; Journal Of Complexity; 29; 3-4; 3-2013; 263-282
0885-064X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/24826
identifier_str_mv Dratman, Ezequiel; Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption; Elsevier; Journal Of Complexity; 29; 3-4; 3-2013; 263-282
0885-064X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0885064X13000186
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2013.03.003
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 13.070432

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