Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes

We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating point arithmetic, the precision of the results is limited by...

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Detalles Bibliográficos
Autores: Antoñana, Mikel, Makazaga Odria, Joseba, Murua, Ander
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/20607
Acceso en línea:http://hdl.handle.net/10810/20607
Access Level:acceso abierto
Palabra clave:symplectic implicit Runge-Kutta methods
fixed-point iteration
stopping criterion
round-off errors
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spelling Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemesAntoñana, MikelMakazaga Odria, JosebaMurua, Andersymplectic implicit Runge-Kutta methodsfixed-point iterationstopping criterionround-off errorsWe propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating point arithmetic, the precision of the results is limited by round-off error propagation. We claim that our implementation with fixed point iteration is near-optimal with respect to round-off error propagation under the assumption that the function that evaluates the right-hand side of the differential equations is implemented with machine numbers (of the prescribed floating point arithmetic) as input and output. In addition, we present a simple procedure to estimate the round-off error propagation by means of a slightly less precise second numerical integration. Some numerical experiments are reported to illustrate the round-off error propagation properties of the proposed implementation.Ministerio de Economía y Comercio: proyecto MTM2013-46553-C3-2-P, Spanish Ministry of Economy and Competitiveness: project MTM2016-76329-R “IMAGEARTH”, Basque Government: Consolidated Research Group IT649-13201720172017info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/20607reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésinfo:eu-repo/grantAgreement/MINECO/MTM2013-46553-C3-2-P/info:eu-repo/grantAgreement/MINECO/MTM2016-76329-R/info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Attribution 4.0 Internationaloai:addi.ehu.eus:10810/206072026-06-18T09:23:17Z
dc.title.none.fl_str_mv Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
title Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
spellingShingle Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
Antoñana, Mikel
symplectic implicit Runge-Kutta methods
fixed-point iteration
stopping criterion
round-off errors
title_short Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
title_full Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
title_fullStr Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
title_full_unstemmed Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
title_sort Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
dc.creator.none.fl_str_mv Antoñana, Mikel
Makazaga Odria, Joseba
Murua, Ander
author Antoñana, Mikel
author_facet Antoñana, Mikel
Makazaga Odria, Joseba
Murua, Ander
author_role author
author2 Makazaga Odria, Joseba
Murua, Ander
author2_role author
author
dc.subject.none.fl_str_mv symplectic implicit Runge-Kutta methods
fixed-point iteration
stopping criterion
round-off errors
topic symplectic implicit Runge-Kutta methods
fixed-point iteration
stopping criterion
round-off errors
description We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating point arithmetic, the precision of the results is limited by round-off error propagation. We claim that our implementation with fixed point iteration is near-optimal with respect to round-off error propagation under the assumption that the function that evaluates the right-hand side of the differential equations is implemented with machine numbers (of the prescribed floating point arithmetic) as input and output. In addition, we present a simple procedure to estimate the round-off error propagation by means of a slightly less precise second numerical integration. Some numerical experiments are reported to illustrate the round-off error propagation properties of the proposed implementation.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/20607
url http://hdl.handle.net/10810/20607
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO/MTM2013-46553-C3-2-P/
info:eu-repo/grantAgreement/MINECO/MTM2016-76329-R/
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Attribution 4.0 International
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Attribution 4.0 International
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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