Computing ODE symmetries as abnormal variational symmetries

Detalhes bibliográficos
Autor(a) principal: Gouveia, Paulo D.F.
Data de Publicação: 2009
Outros Autores: Torres, Delfim F.M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10198/1509
Resumo: We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 387 409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of invariance for abnormal optimal control problems. A computer algebra procedure is developed, which permits one to obtain ODE symmetries by the proposed method. Examples are given, and results compared with those obtained by previous available methods.
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spelling Computing ODE symmetries as abnormal variational symmetriesSymmetriesVariational symmetriesDynamic symmetriesODEsComputer algebra systemsOptimal controlAbnormalityWe give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 387 409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of invariance for abnormal optimal control problems. A computer algebra procedure is developed, which permits one to obtain ODE symmetries by the proposed method. Examples are given, and results compared with those obtained by previous available methods.The authors acknowledge the support from the Portuguese Foundation for Science and Technology (FCT), through the R&D unit Centre for Research on Optimization and Control (CEOC) of the University of Aveiro, cofinanced by the European Community Fund FEDER/POCI 2010. PG is also grateful to the support given by the program PRODEP III/5.3/2003.ElsevierBiblioteca Digital do IPBGouveia, Paulo D.F.Torres, Delfim F.M.2010-01-27T17:58:02Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10198/1509engGouveia, Paulo D.F.; Torres, Delfim F.M. (2009). Computing ODE symmetries as abnormal variational symmetries. Nonlinear Analysis: Theory, Methods & Applications. ISSN 0362-546X. 71:12, p. e138-e146info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-21T10:05:03Zoai:bibliotecadigital.ipb.pt:10198/1509Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:54:54.920847Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Computing ODE symmetries as abnormal variational symmetries
title Computing ODE symmetries as abnormal variational symmetries
spellingShingle Computing ODE symmetries as abnormal variational symmetries
Gouveia, Paulo D.F.
Symmetries
Variational symmetries
Dynamic symmetries
ODEs
Computer algebra systems
Optimal control
Abnormality
title_short Computing ODE symmetries as abnormal variational symmetries
title_full Computing ODE symmetries as abnormal variational symmetries
title_fullStr Computing ODE symmetries as abnormal variational symmetries
title_full_unstemmed Computing ODE symmetries as abnormal variational symmetries
title_sort Computing ODE symmetries as abnormal variational symmetries
author Gouveia, Paulo D.F.
author_facet Gouveia, Paulo D.F.
Torres, Delfim F.M.
author_role author
author2 Torres, Delfim F.M.
author2_role author
dc.contributor.none.fl_str_mv Biblioteca Digital do IPB
dc.contributor.author.fl_str_mv Gouveia, Paulo D.F.
Torres, Delfim F.M.
dc.subject.por.fl_str_mv Symmetries
Variational symmetries
Dynamic symmetries
ODEs
Computer algebra systems
Optimal control
Abnormality
topic Symmetries
Variational symmetries
Dynamic symmetries
ODEs
Computer algebra systems
Optimal control
Abnormality
description We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [P.D.F. Gouveia, D.F.M. Torres, Automatic computation of conservation laws in the calculus of variations and optimal control, Comput. Methods Appl. Math. 5 (4) (2005) 387 409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of invariance for abnormal optimal control problems. A computer algebra procedure is developed, which permits one to obtain ODE symmetries by the proposed method. Examples are given, and results compared with those obtained by previous available methods.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01T00:00:00Z
2010-01-27T17:58:02Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10198/1509
url http://hdl.handle.net/10198/1509
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Gouveia, Paulo D.F.; Torres, Delfim F.M. (2009). Computing ODE symmetries as abnormal variational symmetries. Nonlinear Analysis: Theory, Methods & Applications. ISSN 0362-546X. 71:12, p. e138-e146
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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