Symbolic computation applied to cauchy type singular integrals
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/17619 |
Resumo: | The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system <i>Mathematica</i> to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article. |
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Symbolic computation applied to cauchy type singular integralsSymbolic computationOperator theory algorithmsCauchy projection operatorsSingular integralsWolfram MathematicaThe development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system <i>Mathematica</i> to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article.MDPISapientiaConceição, Ana C.Pires, Jéssica C.2022-02-28T15:50:48Z2021-12-312022-02-24T14:50:03Z2021-12-31T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/17619engMathematical and Computational Applications 27 (1): 3 (2022)2297-874710.3390/mca27010003info: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:RCAAP2024-03-13T02:06:34Zoai:sapientia.ualg.pt:10400.1/17619Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:07:32.931310Repositório 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 |
Symbolic computation applied to cauchy type singular integrals |
title |
Symbolic computation applied to cauchy type singular integrals |
spellingShingle |
Symbolic computation applied to cauchy type singular integrals Conceição, Ana C. Symbolic computation Operator theory algorithms Cauchy projection operators Singular integrals Wolfram Mathematica |
title_short |
Symbolic computation applied to cauchy type singular integrals |
title_full |
Symbolic computation applied to cauchy type singular integrals |
title_fullStr |
Symbolic computation applied to cauchy type singular integrals |
title_full_unstemmed |
Symbolic computation applied to cauchy type singular integrals |
title_sort |
Symbolic computation applied to cauchy type singular integrals |
author |
Conceição, Ana C. |
author_facet |
Conceição, Ana C. Pires, Jéssica C. |
author_role |
author |
author2 |
Pires, Jéssica C. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Conceição, Ana C. Pires, Jéssica C. |
dc.subject.por.fl_str_mv |
Symbolic computation Operator theory algorithms Cauchy projection operators Singular integrals Wolfram Mathematica |
topic |
Symbolic computation Operator theory algorithms Cauchy projection operators Singular integrals Wolfram Mathematica |
description |
The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear transport theory, in the theory of diffraction of acoustic and electromagnetic waves, in the theory of scattering and of inverse scattering, among others. In our work, we use the computer algebra system <i>Mathematica</i> to implement, for the first time on a computer, analytical algorithms developed by us and others within operator theory. The main goal of this paper is to present new operator theory algorithms related to Cauchy type singular integrals, defined in the unit circle. The design of these algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. Several nontrivial examples computed with the algorithms are presented. The corresponding source code of the algorithms has been made available as a supplement to the online edition of this article. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-12-31 2021-12-31T00:00:00Z 2022-02-28T15:50:48Z 2022-02-24T14:50:03Z |
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/10400.1/17619 |
url |
http://hdl.handle.net/10400.1/17619 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Mathematical and Computational Applications 27 (1): 3 (2022) 2297-8747 10.3390/mca27010003 |
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 |
MDPI |
publisher.none.fl_str_mv |
MDPI |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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