Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations

Detalhes bibliográficos
Autor(a) principal: Yazdani,S.
Data de Publicação: 2012
Outros Autores: Hadizadeh,M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000200005
Resumo: In this paper, we compute piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations. The enclosures are in the form of intervals which are guaranteed to contain the exact solution considering all round-off and truncation errors, so the width of interval solutions allows us to control the error estimation. An iterative algorithm to improve the accuracy of initial enclosures is given and its convergence are also investigated. Our numerical experiments show that the precision of interval solutions are reasonable in comparison to the classical methods and the obtained conditions and initial enclosure of the proposed algorithm are not restrictive. Mathematical subject classification: 65G20, 45G10, 65G40.
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spelling Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equationsVolterra-Fredholm integral equationsenclosure methodsinterval analysisguaranteed error boundsIn this paper, we compute piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations. The enclosures are in the form of intervals which are guaranteed to contain the exact solution considering all round-off and truncation errors, so the width of interval solutions allows us to control the error estimation. An iterative algorithm to improve the accuracy of initial enclosures is given and its convergence are also investigated. Our numerical experiments show that the precision of interval solutions are reasonable in comparison to the classical methods and the obtained conditions and initial enclosure of the proposed algorithm are not restrictive. Mathematical subject classification: 65G20, 45G10, 65G40.Sociedade Brasileira de Matemática Aplicada e Computacional2012-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000200005Computational & Applied Mathematics v.31 n.2 2012reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022012000200005info:eu-repo/semantics/openAccessYazdani,S.Hadizadeh,M.eng2012-12-05T00:00:00Zoai:scielo:S1807-03022012000200005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2012-12-05T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
title Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
spellingShingle Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
Yazdani,S.
Volterra-Fredholm integral equations
enclosure methods
interval analysis
guaranteed error bounds
title_short Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
title_full Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
title_fullStr Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
title_full_unstemmed Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
title_sort Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations
author Yazdani,S.
author_facet Yazdani,S.
Hadizadeh,M.
author_role author
author2 Hadizadeh,M.
author2_role author
dc.contributor.author.fl_str_mv Yazdani,S.
Hadizadeh,M.
dc.subject.por.fl_str_mv Volterra-Fredholm integral equations
enclosure methods
interval analysis
guaranteed error bounds
topic Volterra-Fredholm integral equations
enclosure methods
interval analysis
guaranteed error bounds
description In this paper, we compute piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations. The enclosures are in the form of intervals which are guaranteed to contain the exact solution considering all round-off and truncation errors, so the width of interval solutions allows us to control the error estimation. An iterative algorithm to improve the accuracy of initial enclosures is given and its convergence are also investigated. Our numerical experiments show that the precision of interval solutions are reasonable in comparison to the classical methods and the obtained conditions and initial enclosure of the proposed algorithm are not restrictive. Mathematical subject classification: 65G20, 45G10, 65G40.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022012000200005
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022012000200005
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.31 n.2 2012
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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