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...

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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
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openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling 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
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url https://repositorio.unal.edu.co/handle/unal/43499
http://bdigital.unal.edu.co/33597/
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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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dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
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