A modified parametric iteration method for solving nonlinear second order BVPs

Detalhes bibliográficos
Autor(a) principal: Ghorbani,Asghar
Data de Publicação: 2011
Outros Autores: Gachpazan,Morteza, Saberi-Nadjafi,Jafar
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000300002
Resumo: The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.
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spelling A modified parametric iteration method for solving nonlinear second order BVPsmodified parametric iteration methodparametric iteration methodsecond-order boundary value problemsnumerical methodThe original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.Sociedade Brasileira de Matemática Aplicada e Computacional2011-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000300002Computational & Applied Mathematics v.30 n.3 2011reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022011000300002info:eu-repo/semantics/openAccessGhorbani,AsgharGachpazan,MortezaSaberi-Nadjafi,Jafareng2012-01-06T00:00:00Zoai:scielo:S1807-03022011000300002Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2012-01-06T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv A modified parametric iteration method for solving nonlinear second order BVPs
title A modified parametric iteration method for solving nonlinear second order BVPs
spellingShingle A modified parametric iteration method for solving nonlinear second order BVPs
Ghorbani,Asghar
modified parametric iteration method
parametric iteration method
second-order boundary value problems
numerical method
title_short A modified parametric iteration method for solving nonlinear second order BVPs
title_full A modified parametric iteration method for solving nonlinear second order BVPs
title_fullStr A modified parametric iteration method for solving nonlinear second order BVPs
title_full_unstemmed A modified parametric iteration method for solving nonlinear second order BVPs
title_sort A modified parametric iteration method for solving nonlinear second order BVPs
author Ghorbani,Asghar
author_facet Ghorbani,Asghar
Gachpazan,Morteza
Saberi-Nadjafi,Jafar
author_role author
author2 Gachpazan,Morteza
Saberi-Nadjafi,Jafar
author2_role author
author
dc.contributor.author.fl_str_mv Ghorbani,Asghar
Gachpazan,Morteza
Saberi-Nadjafi,Jafar
dc.subject.por.fl_str_mv modified parametric iteration method
parametric iteration method
second-order boundary value problems
numerical method
topic modified parametric iteration method
parametric iteration method
second-order boundary value problems
numerical method
description The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000300002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000300002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022011000300002
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.30 n.3 2011
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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