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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/46558
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:44:53Zoai: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:34982025-09-29 09:44:53.491CONICET 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 |
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1844613412410097664 |
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13.070432 |