Newton's method and a mesh independence principle for certain semilinear boundary value problems

Autores
Dratman, Ezequiel; Matera, Guillermo
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We exhibit an algorithm which computes an ϵ-approximation of the positive solutions of a family of boundary-value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a finite-dimensional Newton iteration associated with a suitable discretized version of the problem under consideration. To determine the behavior of such a discrete iteration we establish an explicit mesh-independence principle. We apply a homotopy-continuation algorithm to compute a starting point of the discrete Newton iteration, and the discrete Newton iteration until an ϵ-approximation of the stationary solution is obtained. The algorithm performs roughly O((1/ϵ)1/2 ) flops and function evaluations.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Boundary-Value Problems
Neumann Boundary Conditions
Newton'S Method
Mesh-Independence Principle
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/46558
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/46558
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Newton's method and a mesh independence principle for certain semilinear boundary value problemsDratman, EzequielMatera, GuillermoBoundary-Value ProblemsNeumann Boundary ConditionsNewton'S MethodMesh-Independence Principlehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We exhibit an algorithm which computes an ϵ-approximation of the positive solutions of a family of boundary-value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a finite-dimensional Newton iteration associated with a suitable discretized version of the problem under consideration. To determine the behavior of such a discrete iteration we establish an explicit mesh-independence principle. We apply a homotopy-continuation algorithm to compute a starting point of the discrete Newton iteration, and the discrete Newton iteration until an ϵ-approximation of the stationary solution is obtained. The algorithm performs roughly O((1/ϵ)1/2 ) flops and function evaluations.Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/46558Dratman, Ezequiel; Matera, Guillermo; Newton's method and a mesh independence principle for certain semilinear boundary value problems; Elsevier Science; Journal Of Computational And Applied Mathematics; 292; 1-2016; 188-2120377-0427CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0377042715003532info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2015.07.004info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:13:46Zoai:ri.conicet.gov.ar:11336/46558instacron: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 11:13:46.862CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Newton's method and a mesh independence principle for certain semilinear boundary value problems
title Newton's method and a mesh independence principle for certain semilinear boundary value problems
spellingShingle Newton's method and a mesh independence principle for certain semilinear boundary value problems
Dratman, Ezequiel
Boundary-Value Problems
Neumann Boundary Conditions
Newton'S Method
Mesh-Independence Principle
title_short Newton's method and a mesh independence principle for certain semilinear boundary value problems
title_full Newton's method and a mesh independence principle for certain semilinear boundary value problems
title_fullStr Newton's method and a mesh independence principle for certain semilinear boundary value problems
title_full_unstemmed Newton's method and a mesh independence principle for certain semilinear boundary value problems
title_sort Newton's method and a mesh independence principle for certain semilinear boundary value problems
dc.creator.none.fl_str_mv Dratman, Ezequiel
Matera, Guillermo
author Dratman, Ezequiel
author_facet Dratman, Ezequiel
Matera, Guillermo
author_role author
author2 Matera, Guillermo
author2_role author
dc.subject.none.fl_str_mv Boundary-Value Problems
Neumann Boundary Conditions
Newton'S Method
Mesh-Independence Principle
topic Boundary-Value Problems
Neumann Boundary Conditions
Newton'S Method
Mesh-Independence Principle
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 exhibit an algorithm which computes an ϵ-approximation of the positive solutions of a family of boundary-value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a finite-dimensional Newton iteration associated with a suitable discretized version of the problem under consideration. To determine the behavior of such a discrete iteration we establish an explicit mesh-independence principle. We apply a homotopy-continuation algorithm to compute a starting point of the discrete Newton iteration, and the discrete Newton iteration until an ϵ-approximation of the stationary solution is obtained. The algorithm performs roughly O((1/ϵ)1/2 ) flops and function evaluations.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We exhibit an algorithm which computes an ϵ-approximation of the positive solutions of a family of boundary-value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a finite-dimensional Newton iteration associated with a suitable discretized version of the problem under consideration. To determine the behavior of such a discrete iteration we establish an explicit mesh-independence principle. We apply a homotopy-continuation algorithm to compute a starting point of the discrete Newton iteration, and the discrete Newton iteration until an ϵ-approximation of the stationary solution is obtained. The algorithm performs roughly O((1/ϵ)1/2 ) flops and function evaluations.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
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/11336/46558
Dratman, Ezequiel; Matera, Guillermo; Newton's method and a mesh independence principle for certain semilinear boundary value problems; Elsevier Science; Journal Of Computational And Applied Mathematics; 292; 1-2016; 188-212
0377-0427
CONICET Digital
CONICET
url http://hdl.handle.net/11336/46558
identifier_str_mv Dratman, Ezequiel; Matera, Guillermo; Newton's method and a mesh independence principle for certain semilinear boundary value problems; Elsevier Science; Journal Of Computational And Applied Mathematics; 292; 1-2016; 188-212
0377-0427
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/S0377042715003532
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2015.07.004
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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
_version_ 1846781550079770624
score 12.982451

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