General splitting methods for abstract semilinear evolution equations

Autores
Borgna, Juan Pablo; de Leo, Mariano Fernando; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schr¨odinger, Schr¨odinger–Poisson, Gross– Pitaevskii equations, etc. This picture includes as particular instances known schemes such as LieTrotter, Strang, and Ruth–Yoshida. The convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity, we show the linear convergence of these methods. We finally mention that in some special cases in which the linear convergence result is known, the assumptions we made are less restrictive.
Fil: Borgna, Juan Pablo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: de Leo, Mariano Fernando. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Lie-Trotter
Splitting Integrators
Semilinear Problems
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:11336/20971
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/20971
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling General splitting methods for abstract semilinear evolution equationsBorgna, Juan Pablode Leo, Mariano FernandoRial, Diego FernandoSanchez Fernandez de la Vega, Constanza MarielLie-TrotterSplitting IntegratorsSemilinear Problemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schr¨odinger, Schr¨odinger–Poisson, Gross– Pitaevskii equations, etc. This picture includes as particular instances known schemes such as LieTrotter, Strang, and Ruth–Yoshida. The convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity, we show the linear convergence of these methods. We finally mention that in some special cases in which the linear convergence result is known, the assumptions we made are less restrictive.Fil: Borgna, Juan Pablo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: de Leo, Mariano Fernando. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Sanchez Fernandez de la Vega, Constanza Mariel. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaInternational Press Boston2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/20971Borgna, Juan Pablo; de Leo, Mariano Fernando; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; General splitting methods for abstract semilinear evolution equations; International Press Boston; Communications in Mathematical Sciences; 13; 1; 1-2015; 83-1011539-6746CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4310/CMS.2015.v13.n1.a4info:eu-repo/semantics/altIdentifier/url/http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0013/0001/a004/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:17:29Zoai:ri.conicet.gov.ar:11336/20971instacron: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:34982025-09-10 13:17:29.565CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv General splitting methods for abstract semilinear evolution equations
title General splitting methods for abstract semilinear evolution equations
spellingShingle General splitting methods for abstract semilinear evolution equations
Borgna, Juan Pablo
Lie-Trotter
Splitting Integrators
Semilinear Problems
title_short General splitting methods for abstract semilinear evolution equations
title_full General splitting methods for abstract semilinear evolution equations
title_fullStr General splitting methods for abstract semilinear evolution equations
title_full_unstemmed General splitting methods for abstract semilinear evolution equations
title_sort General splitting methods for abstract semilinear evolution equations
dc.creator.none.fl_str_mv Borgna, Juan Pablo
de Leo, Mariano Fernando
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
author Borgna, Juan Pablo
author_facet Borgna, Juan Pablo
de Leo, Mariano Fernando
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
author_role author
author2 de Leo, Mariano Fernando
Rial, Diego Fernando
Sanchez Fernandez de la Vega, Constanza Mariel
author2_role author
author
author
dc.subject.none.fl_str_mv Lie-Trotter
Splitting Integrators
Semilinear Problems
topic Lie-Trotter
Splitting Integrators
Semilinear Problems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schr¨odinger, Schr¨odinger–Poisson, Gross– Pitaevskii equations, etc. This picture includes as particular instances known schemes such as LieTrotter, Strang, and Ruth–Yoshida. The convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity, we show the linear convergence of these methods. We finally mention that in some special cases in which the linear convergence result is known, the assumptions we made are less restrictive.
Fil: Borgna, Juan Pablo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: de Leo, Mariano Fernando. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we present a unified picture concerning general splitting methods for solving a large class of semilinear problems: nonlinear Schr¨odinger, Schr¨odinger–Poisson, Gross– Pitaevskii equations, etc. This picture includes as particular instances known schemes such as LieTrotter, Strang, and Ruth–Yoshida. The convergence result is presented in suitable Hilbert spaces related to the time regularity of the solution and is based on Lipschitz estimates for the nonlinearity. In addition, with extra requirements both on the regularity of the initial datum and on the nonlinearity, we show the linear convergence of these methods. We finally mention that in some special cases in which the linear convergence result is known, the assumptions we made are less restrictive.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/20971
Borgna, Juan Pablo; de Leo, Mariano Fernando; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; General splitting methods for abstract semilinear evolution equations; International Press Boston; Communications in Mathematical Sciences; 13; 1; 1-2015; 83-101
1539-6746
CONICET Digital
CONICET
url http://hdl.handle.net/11336/20971
identifier_str_mv Borgna, Juan Pablo; de Leo, Mariano Fernando; Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; General splitting methods for abstract semilinear evolution equations; International Press Boston; Communications in Mathematical Sciences; 13; 1; 1-2015; 83-101
1539-6746
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4310/CMS.2015.v13.n1.a4
info:eu-repo/semantics/altIdentifier/url/http://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0013/0001/a004/
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv International Press Boston
publisher.none.fl_str_mv International Press Boston
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 13.004268

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