Operational Tau approximation for a general class of fractional integro-differential equations
Autor(a) principal: | |
---|---|
Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000300010 |
Resumo: | In this work, an extension of the algebraic formulation of the operational Tau method (OTM) for the numerical solution of the linear and nonlinear fractional integro-differential equations (FIDEs) is proposed. The main idea behind the OTM is to convert the fractional differential and integral parts of the desired FIDE to some operational matrices. Then the FIDE reduces to a set of algebraic equations. We demonstrate the Tau matrix representation for solving FIDEs based on arbitrary orthogonal polynomials. Some advantages of using the method, errorestimation and computer algorithm are also presented. Illustrative linear and nonlinear experiments are included to show the validity and applicability of the presented method. Mathematical subject classification: 65M70, 34A25, 26A33, 47Gxx. |
id |
SBMAC-2_21ae186eb002d5a0fddb38cda76164fa |
---|---|
oai_identifier_str |
oai:scielo:S1807-03022011000300010 |
network_acronym_str |
SBMAC-2 |
network_name_str |
Computational & Applied Mathematics |
repository_id_str |
|
spelling |
Operational Tau approximation for a general class of fractional integro-differential equationsspectral methodsoperational Tau methodfractional integro-differential equationserror estimationcomputer algorithm of the methodIn this work, an extension of the algebraic formulation of the operational Tau method (OTM) for the numerical solution of the linear and nonlinear fractional integro-differential equations (FIDEs) is proposed. The main idea behind the OTM is to convert the fractional differential and integral parts of the desired FIDE to some operational matrices. Then the FIDE reduces to a set of algebraic equations. We demonstrate the Tau matrix representation for solving FIDEs based on arbitrary orthogonal polynomials. Some advantages of using the method, errorestimation and computer algorithm are also presented. Illustrative linear and nonlinear experiments are included to show the validity and applicability of the presented method. Mathematical subject classification: 65M70, 34A25, 26A33, 47Gxx.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=S1807-03022011000300010Computational & Applied Mathematics v.30 n.3 2011reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022011000300010info:eu-repo/semantics/openAccessVanani,S. KarimiAminataei,A.eng2012-01-06T00:00:00Zoai:scielo:S1807-03022011000300010Revistahttps://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 |
Operational Tau approximation for a general class of fractional integro-differential equations |
title |
Operational Tau approximation for a general class of fractional integro-differential equations |
spellingShingle |
Operational Tau approximation for a general class of fractional integro-differential equations Vanani,S. Karimi spectral methods operational Tau method fractional integro-differential equations error estimation computer algorithm of the method |
title_short |
Operational Tau approximation for a general class of fractional integro-differential equations |
title_full |
Operational Tau approximation for a general class of fractional integro-differential equations |
title_fullStr |
Operational Tau approximation for a general class of fractional integro-differential equations |
title_full_unstemmed |
Operational Tau approximation for a general class of fractional integro-differential equations |
title_sort |
Operational Tau approximation for a general class of fractional integro-differential equations |
author |
Vanani,S. Karimi |
author_facet |
Vanani,S. Karimi Aminataei,A. |
author_role |
author |
author2 |
Aminataei,A. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Vanani,S. Karimi Aminataei,A. |
dc.subject.por.fl_str_mv |
spectral methods operational Tau method fractional integro-differential equations error estimation computer algorithm of the method |
topic |
spectral methods operational Tau method fractional integro-differential equations error estimation computer algorithm of the method |
description |
In this work, an extension of the algebraic formulation of the operational Tau method (OTM) for the numerical solution of the linear and nonlinear fractional integro-differential equations (FIDEs) is proposed. The main idea behind the OTM is to convert the fractional differential and integral parts of the desired FIDE to some operational matrices. Then the FIDE reduces to a set of algebraic equations. We demonstrate the Tau matrix representation for solving FIDEs based on arbitrary orthogonal polynomials. Some advantages of using the method, errorestimation and computer algorithm are also presented. Illustrative linear and nonlinear experiments are included to show the validity and applicability of the presented method. Mathematical subject classification: 65M70, 34A25, 26A33, 47Gxx. |
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=S1807-03022011000300010 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022011000300010 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1807-03022011000300010 |
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 |
_version_ |
1754734890326163456 |