Rosenbrock type methods for solving non-linear second-order in time problems

In this work we present a new class of methods which have been developed in order to numerically solve non-linear second-order in time problems. These methods are of Rosenbrock type, and can be seen as a generalization of these methods when they are applied to second-order in time problems which hav...

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Author: Moreta Santos, María Jesús
Format: article
Publication Date:2017
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/17938
Online Access:https://hdl.handle.net/20.500.14352/17938
Access Level:Open access
Keyword:Rosenbrock-Nystr¨om methods
Runge-Kutta-Nystr¨om methods.
Matemáticas (Matemáticas)
12 Matemáticas
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oai_identifier_str oai:docta.ucm.es:20.500.14352/17938
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repository_id_str
spelling Rosenbrock type methods for solving non-linear second-order in time problemsMoreta Santos, María JesúsRosenbrock-Nystr¨om methodsRunge-Kutta-Nystr¨om methods.Matemáticas (Matemáticas)12 MatemáticasIn this work we present a new class of methods which have been developed in order to numerically solve non-linear second-order in time problems. These methods are of Rosenbrock type, and can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they follow the ideas of Runge-Kutta-Nystr¨om methods when solving second-order in time problems, we will call them Rosenbrock-Nystr¨om methods. These new methods present less computational cost than implicit RungeKutta-Nystr¨om ones, as the non-linear systems which arises when RungeKutta-Nystr¨om methods are used are replaced with sequences of linear ones. In this article we show the development of Rosenbrock-Nystr¨om methods, as well as the conditions that must be satisfied to get the desired classical order (up to order four) and the main ideas in order to have stability. Besides, we will show some numerical experiments that prove the good behaviour of these new methods.Universidad Complutense de Madrid20172017-07-1320172017-07-13journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/17938reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/179382026-06-02T12:44:21Z
dc.title.none.fl_str_mv Rosenbrock type methods for solving non-linear second-order in time problems
title Rosenbrock type methods for solving non-linear second-order in time problems
spellingShingle Rosenbrock type methods for solving non-linear second-order in time problems
Moreta Santos, María Jesús
Rosenbrock-Nystr¨om methods
Runge-Kutta-Nystr¨om methods.
Matemáticas (Matemáticas)
12 Matemáticas
title_short Rosenbrock type methods for solving non-linear second-order in time problems
title_full Rosenbrock type methods for solving non-linear second-order in time problems
title_fullStr Rosenbrock type methods for solving non-linear second-order in time problems
title_full_unstemmed Rosenbrock type methods for solving non-linear second-order in time problems
title_sort Rosenbrock type methods for solving non-linear second-order in time problems
dc.creator.none.fl_str_mv Moreta Santos, María Jesús
author Moreta Santos, María Jesús
author_facet Moreta Santos, María Jesús
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Rosenbrock-Nystr¨om methods
Runge-Kutta-Nystr¨om methods.
Matemáticas (Matemáticas)
12 Matemáticas
topic Rosenbrock-Nystr¨om methods
Runge-Kutta-Nystr¨om methods.
Matemáticas (Matemáticas)
12 Matemáticas
description In this work we present a new class of methods which have been developed in order to numerically solve non-linear second-order in time problems. These methods are of Rosenbrock type, and can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they follow the ideas of Runge-Kutta-Nystr¨om methods when solving second-order in time problems, we will call them Rosenbrock-Nystr¨om methods. These new methods present less computational cost than implicit RungeKutta-Nystr¨om ones, as the non-linear systems which arises when RungeKutta-Nystr¨om methods are used are replaced with sequences of linear ones. In this article we show the development of Rosenbrock-Nystr¨om methods, as well as the conditions that must be satisfied to get the desired classical order (up to order four) and the main ideas in order to have stability. Besides, we will show some numerical experiments that prove the good behaviour of these new methods.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-07-13
2017
2017-07-13
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/17938
url https://hdl.handle.net/20.500.14352/17938
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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