Analysis and spectral element solution of nonlinear integral equations of hammerstein type
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Capítulo de livro |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-3-030-65509-9_2 http://hdl.handle.net/11449/206065 |
Resumo: | We employ the spectral element method with Gauss-Lobatto-Legendre collocation points to approximate nonlinear integral equations of Hammerstein type. Using the Banach Fixed Point Theorem, we establish sufficient conditions for the existence and uniqueness of solutions in the L2 norm, as well as the convergence of the proposed method, under a different aspect of the existing works in the literature, indicating that the numerical error decays exponentially provided that the kernel function be smooth enough. The iterative Picard process was used to approximate the nonlinear problem. Numerical experiments involving one- and two-dimensional nonlinear equations illustrate the effectiveness of this approach. |
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Repositório Institucional da UNESP |
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Analysis and spectral element solution of nonlinear integral equations of hammerstein typeNonlinear Hammerstein integral equationsPicard iterationSpectral element methodWe employ the spectral element method with Gauss-Lobatto-Legendre collocation points to approximate nonlinear integral equations of Hammerstein type. Using the Banach Fixed Point Theorem, we establish sufficient conditions for the existence and uniqueness of solutions in the L2 norm, as well as the convergence of the proposed method, under a different aspect of the existing works in the literature, indicating that the numerical error decays exponentially provided that the kernel function be smooth enough. The iterative Picard process was used to approximate the nonlinear problem. Numerical experiments involving one- and two-dimensional nonlinear equations illustrate the effectiveness of this approach.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)ICTI-UFBA CentroDMAT-UFPR and INCT-GPUniversidade Estadual Paulista (UNESP) IGCECETEC-UFRB CentroUniversidade Estadual Paulista (UNESP) IGCECNPq: 313100/2017-9Universidade Federal da Bahia (UFBA)Universidade Federal do Paraná (UFPR)Universidade Estadual Paulista (Unesp)CETEC-UFRB CentroAzevedo, Juarez S.Oliveira, Saulo P.Afonso, Suzete M. [UNESP]da Silva, Mariana P. G.2021-06-25T10:25:56Z2021-06-25T10:25:56Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart41-62http://dx.doi.org/10.1007/978-3-030-65509-9_2Studies in Systems, Decision and Control, v. 340, p. 41-62.2198-41902198-4182http://hdl.handle.net/11449/20606510.1007/978-3-030-65509-9_22-s2.0-85102732120Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengStudies in Systems, Decision and Controlinfo:eu-repo/semantics/openAccess2021-10-22T20:48:59Zoai:repositorio.unesp.br:11449/206065Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:52:03.090022Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
title |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
spellingShingle |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type Azevedo, Juarez S. Nonlinear Hammerstein integral equations Picard iteration Spectral element method |
title_short |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
title_full |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
title_fullStr |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
title_full_unstemmed |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
title_sort |
Analysis and spectral element solution of nonlinear integral equations of hammerstein type |
author |
Azevedo, Juarez S. |
author_facet |
Azevedo, Juarez S. Oliveira, Saulo P. Afonso, Suzete M. [UNESP] da Silva, Mariana P. G. |
author_role |
author |
author2 |
Oliveira, Saulo P. Afonso, Suzete M. [UNESP] da Silva, Mariana P. G. |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Federal da Bahia (UFBA) Universidade Federal do Paraná (UFPR) Universidade Estadual Paulista (Unesp) CETEC-UFRB Centro |
dc.contributor.author.fl_str_mv |
Azevedo, Juarez S. Oliveira, Saulo P. Afonso, Suzete M. [UNESP] da Silva, Mariana P. G. |
dc.subject.por.fl_str_mv |
Nonlinear Hammerstein integral equations Picard iteration Spectral element method |
topic |
Nonlinear Hammerstein integral equations Picard iteration Spectral element method |
description |
We employ the spectral element method with Gauss-Lobatto-Legendre collocation points to approximate nonlinear integral equations of Hammerstein type. Using the Banach Fixed Point Theorem, we establish sufficient conditions for the existence and uniqueness of solutions in the L2 norm, as well as the convergence of the proposed method, under a different aspect of the existing works in the literature, indicating that the numerical error decays exponentially provided that the kernel function be smooth enough. The iterative Picard process was used to approximate the nonlinear problem. Numerical experiments involving one- and two-dimensional nonlinear equations illustrate the effectiveness of this approach. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T10:25:56Z 2021-06-25T10:25:56Z 2021-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/bookPart |
format |
bookPart |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-3-030-65509-9_2 Studies in Systems, Decision and Control, v. 340, p. 41-62. 2198-4190 2198-4182 http://hdl.handle.net/11449/206065 10.1007/978-3-030-65509-9_2 2-s2.0-85102732120 |
url |
http://dx.doi.org/10.1007/978-3-030-65509-9_2 http://hdl.handle.net/11449/206065 |
identifier_str_mv |
Studies in Systems, Decision and Control, v. 340, p. 41-62. 2198-4190 2198-4182 10.1007/978-3-030-65509-9_2 2-s2.0-85102732120 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Studies in Systems, Decision and Control |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
41-62 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128713393438720 |