The numerical solution of linear time-varying daes with index 2 by irk methods
Differential-algebraic equations (DAEs) with a higher index can be approximated by implicit Runge-Kutta methods (IRK). Until now,.a number of initial value problems have been approximated by Runge-Kutta methods, but all these problems have a special semi-explicit or Hessenberg form. In the present p...
- Autores:
-
Izquierdo, Ebroul
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1994
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43499
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43499
http://bdigital.unal.edu.co/33597/
- Palabra clave:
- Ordinary differential equations
differential-algebraic equations
initial value problems
implicit Runge-Kutta methods
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Izquierdo, Ebroul589db2aa-9db4-4dd2-9848-656efca3ffbe3002019-06-28T12:03:26Z2019-06-28T12:03:26Z1994https://repositorio.unal.edu.co/handle/unal/43499http://bdigital.unal.edu.co/33597/Differential-algebraic equations (DAEs) with a higher index can be approximated by implicit Runge-Kutta methods (IRK). Until now,.a number of initial value problems have been approximated by Runge-Kutta methods, but all these problems have a special semi-explicit or Hessenberg form. In the present paper we consider IRK methods applied to general linear time-varying (nonautonomous) DAEs tractable with index 2. For some stiffly accurate IRK formulas we show that the order of accuracy in the differential component is the same nonstiff order, if the DAE has constant nullspace. We prove that IRK methods cannot be feasible or become exponentially unstable when applied to linear DAEs with variable nullspace. In order to overcome these difficulties we propose a new approach for this case. Feasibility, weak instability and convergence are proved. Order results are given in terms of the Butcher identities.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/33472Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 28, núm. 2 (1994); 43-82 0034-7426Izquierdo, Ebroul (1994) The numerical solution of linear time-varying daes with index 2 by irk methods. Revista Colombiana de Matemáticas; Vol. 28, núm. 2 (1994); 43-82 0034-7426 .The numerical solution of linear time-varying daes with index 2 by irk methodsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTOrdinary differential equationsdifferential-algebraic equationsinitial value problemsimplicit Runge-Kutta methodsORIGINAL33472-124170-1-PB.pdfapplication/pdf12249836https://repositorio.unal.edu.co/bitstream/unal/43499/1/33472-124170-1-PB.pdf96f69f25b566fa590b72367f889d9739MD51THUMBNAIL33472-124170-1-PB.pdf.jpg33472-124170-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg7003https://repositorio.unal.edu.co/bitstream/unal/43499/2/33472-124170-1-PB.pdf.jpg0b2f77b3de70414a3c1bfd4487959841MD52unal/43499oai:repositorio.unal.edu.co:unal/434992023-02-12 23:04:47.39Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
dc.title.spa.fl_str_mv |
The numerical solution of linear time-varying daes with index 2 by irk methods |
title |
The numerical solution of linear time-varying daes with index 2 by irk methods |
spellingShingle |
The numerical solution of linear time-varying daes with index 2 by irk methods Ordinary differential equations differential-algebraic equations initial value problems implicit Runge-Kutta methods |
title_short |
The numerical solution of linear time-varying daes with index 2 by irk methods |
title_full |
The numerical solution of linear time-varying daes with index 2 by irk methods |
title_fullStr |
The numerical solution of linear time-varying daes with index 2 by irk methods |
title_full_unstemmed |
The numerical solution of linear time-varying daes with index 2 by irk methods |
title_sort |
The numerical solution of linear time-varying daes with index 2 by irk methods |
dc.creator.fl_str_mv |
Izquierdo, Ebroul |
dc.contributor.author.spa.fl_str_mv |
Izquierdo, Ebroul |
dc.subject.proposal.spa.fl_str_mv |
Ordinary differential equations differential-algebraic equations initial value problems implicit Runge-Kutta methods |
topic |
Ordinary differential equations differential-algebraic equations initial value problems implicit Runge-Kutta methods |
description |
Differential-algebraic equations (DAEs) with a higher index can be approximated by implicit Runge-Kutta methods (IRK). Until now,.a number of initial value problems have been approximated by Runge-Kutta methods, but all these problems have a special semi-explicit or Hessenberg form. In the present paper we consider IRK methods applied to general linear time-varying (nonautonomous) DAEs tractable with index 2. For some stiffly accurate IRK formulas we show that the order of accuracy in the differential component is the same nonstiff order, if the DAE has constant nullspace. We prove that IRK methods cannot be feasible or become exponentially unstable when applied to linear DAEs with variable nullspace. In order to overcome these difficulties we propose a new approach for this case. Feasibility, weak instability and convergence are proved. Order results are given in terms of the Butcher identities. |
publishDate |
1994 |
dc.date.issued.spa.fl_str_mv |
1994 |
dc.date.accessioned.spa.fl_str_mv |
2019-06-28T12:03:26Z |
dc.date.available.spa.fl_str_mv |
2019-06-28T12:03:26Z |
dc.type.spa.fl_str_mv |
Artículo de revista |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.content.spa.fl_str_mv |
Text |
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http://purl.org/redcol/resource_type/ART |
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http://purl.org/coar/resource_type/c_6501 |
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publishedVersion |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/43499 |
dc.identifier.eprints.spa.fl_str_mv |
http://bdigital.unal.edu.co/33597/ |
url |
https://repositorio.unal.edu.co/handle/unal/43499 http://bdigital.unal.edu.co/33597/ |
dc.language.iso.spa.fl_str_mv |
spa |
language |
spa |
dc.relation.spa.fl_str_mv |
http://revistas.unal.edu.co/index.php/recolma/article/view/33472 |
dc.relation.ispartof.spa.fl_str_mv |
Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
dc.relation.ispartofseries.none.fl_str_mv |
Revista Colombiana de Matemáticas; Vol. 28, núm. 2 (1994); 43-82 0034-7426 |
dc.relation.references.spa.fl_str_mv |
Izquierdo, Ebroul (1994) The numerical solution of linear time-varying daes with index 2 by irk methods. Revista Colombiana de Matemáticas; Vol. 28, núm. 2 (1994); 43-82 0034-7426 . |
dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
dc.rights.license.spa.fl_str_mv |
Atribución-NoComercial 4.0 Internacional |
dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc/4.0/ |
dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
eu_rights_str_mv |
openAccess |
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application/pdf |
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Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas |
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Universidad Nacional de Colombia |
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