Publication
Computing ODE symmetries as abnormal variational symmetries
| Summary: | 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. |
|---|---|
| Main Authors: | Gouveia, Paulo D.F. |
| Other Authors: | Torres, Delfim F.M. |
| Subject: | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| Year: | 2009 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade Politécnica de Bragança |
| Language: | English |
| Origin: | Biblioteca Digital da UPB |
| _version_ | 1877782580806287360 |
|---|---|
| author | Gouveia, Paulo D.F. |
| author2 | Torres, Delfim F.M. |
| author2_role | author |
| author_facet | Gouveia, Paulo D.F. Torres, Delfim F.M. |
| author_role | author |
| contributor_name_str_mv | Biblioteca Digital da UPB |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Gouveia, Paulo D.F.\",\"Person.identifier.orcid\":\"0000-0003-3049-6230\",\"Person.identifier.scopusAuthorID\":\"20433578000\"},{\"Person.name\":\"Torres, Delfim F.M.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Biblioteca Digital da UPB |
| datacite.creators.creator.creatorName.fl_str_mv | Gouveia, Paulo D.F. Torres, Delfim F.M. |
| datacite.date.Accepted.fl_str_mv | 2009-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2010-01-27T17:58:02Z |
| datacite.date.embargoed.fl_str_mv | 2010-01-27T17:58:02Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| datacite.titles.title.fl_str_mv | Computing ODE symmetries as abnormal variational symmetries |
| dc.contributor.none.fl_str_mv | Biblioteca Digital da UPB |
| dc.creator.none.fl_str_mv | Gouveia, Paulo D.F. Torres, Delfim F.M. |
| dc.date.Accepted.fl_str_mv | 2009-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2010-01-27T17:58:02Z |
| dc.date.embargoed.fl_str_mv | 2010-01-27T17:58:02Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10198/1509 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| dc.title.fl_str_mv | Computing ODE symmetries as abnormal variational symmetries |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| 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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://bibliotecadigital.unipb.pt/bitstreams/850d315a-a9e9-433a-b4cf-83c321d0db66/download |
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| identifier.url.fl_str_mv | http://hdl.handle.net/10198/1509 |
| inst_facet_str | urn:organizationAcronym:unipb{{{_:::_}}}Universidade Politécnica de Bragança |
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| institution | Universidade Politécnica de Bragança |
| instname_str | Universidade Politécnica de Bragança |
| language | eng |
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| network_name_str | Biblioteca Digital da UPB |
| oai_identifier_str | oai:bibliotecadigital.unipb.pt:10198/1509 |
| organization_str_mv | urn:organizationAcronym:unipb |
| person_str_mv | Gouveia, Paulo D.F. Gouveia, Paulo D.F. http://orcid.org/0000-0003-3049-6230 0000-0003-3049-6230 Torres, Delfim F.M. |
| publishDate | 2009 |
| publisher.none.fl_str_mv | Elsevier |
| repo_facet_str | urn:repositoryAcronym:ipb{{{_:::_}}}Biblioteca Digital da UPB |
| reponame_str | Biblioteca Digital da UPB |
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| spelling | engElsevierptWe 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.application/pdfptComputing ODE symmetries as abnormal variational symmetriesPersonalGouveia, Paulo D.F.DSpacehttp://dspace.org/items/41c37437-90c4-4e40-893b-44fe4ae1f159DSpacehttp://dspace.org/items/41c37437-90c4-4e40-893b-44fe4ae1f159GouveiaPaulo D.F.ORCIDhttp://orcid.org0000-0003-3049-6230Scopus Author IDhttps://www.scopus.com20433578000Torres, Delfim F.M.HostingInstitutionOrganizationalBiblioteca Digital da UPBe-mailmailto:dspace@unipb.ptdspace@unipb.pt2010-01-27T17:58:02Z20092009-01-01T00:00:00ZHandlehttp://hdl.handle.net/10198/1509http://purl.org/coar/access_right/c_abf2open accessSymmetriesVariational symmetriesDynamic symmetriesODEsComputer algebra systemsOptimal controlAbnormality213909 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://bibliotecadigital.unipb.pt/bitstreams/850d315a-a9e9-433a-b4cf-83c321d0db66/downloadNonlinear Analysis: Theory, Methods & Applications71(12)e138e146 |
| spellingShingle | Computing ODE symmetries as abnormal variational symmetries Gouveia, Paulo D.F. Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| status | SINGLETON |
| subject.fl_str_mv | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| title | 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_short | Computing ODE symmetries as abnormal variational symmetries |
| title_sort | Computing ODE symmetries as abnormal variational symmetries |
| topic | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| topic_facet | Symmetries Variational symmetries Dynamic symmetries ODEs Computer algebra systems Optimal control Abnormality |
| url | http://hdl.handle.net/10198/1509 |
| visible | 1 |
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