Generalized TASE-RK methods for stiff problems

A family of Time-Accurate and Stable Explicit (TASE) methods for the numerical integration of Initial Value Problems in stiff Ordinary Differential Equations (ODEs) y ′(t) = f(t, y) was recently introduced in [1]. The main idea was to make local extrapolation of a stabilized Euler method. More recen...

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Detalles Bibliográficos
Autores: Hernández Abreu, Domingo, Gonz´alez Pinto, Pagano, G., P´erez Rodr´ıguez, S.
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad de La Laguna (ULL)
Repositorio:RIULL. Repositorio Institucional de la Universidad de La Laguna
OAI Identifier:oai:riull.ull.es:915/39027
Acceso en línea:http://riull.ull.es/xmlui/handle/915/39027
Access Level:acceso abierto
Palabra clave:Explicit Runge-Kutta methods
TASE-RK methods
W-methods
Rosenbrock methods
Time Integration
Stability
Stiffness
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spelling Generalized TASE-RK methods for stiff problemsHernández Abreu, DomingoGonz´alez PintoPagano, G.P´erez Rodr´ıguez, S.Explicit Runge-Kutta methodsTASE-RK methodsW-methodsRosenbrock methodsTime IntegrationStabilityStiffnessA family of Time-Accurate and Stable Explicit (TASE) methods for the numerical integration of Initial Value Problems in stiff Ordinary Differential Equations (ODEs) y ′(t) = f(t, y) was recently introduced in [1]. The main idea was to make local extrapolation of a stabilized Euler method. More recently, in [3] a similar approach by considering the stabilization of arbitrary explicit Runge-Kutta methods (TASE-RK) was analyzed. In this case the explicit Runge-Kutta method integrates a transformed ODE obtained by multiplying the vector field f(t, y) by a certain operator which approximates the identity mapping up to a given order p. The main inconvenience of both approaches is that to reach order p the solution of p2 linear systems plus the evaluation of p derivatives are required per integration step. In order to substantially reduce the computational costs of the former approaches in the linear system solution, but maintaining the good accuracy and stability properties, a new family of TASE-RK methods which allow to introduce a few more free parameters are considered. The formulation of the methods was conceived to be implemented not only in sequential mode but it admits parallelism in a straigthforward way. Furthermore, since these methods are linearly implicit, connections to the class of W-methods [19] are properly established. The order conditions for the new class of methods are widely studied by using the rooted tree theory. For p = 3, 4, new methods with p sequential stages and order p are derived and compared on semidiscrete 1D and 2D Partial Differential Equations (PDEs) to those in [1, 3] and other standard Rosenbrock and W-methods in the literature.Análisis MatemáticoGrupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/202420242023info:eu-repo/semantics/articleapplication/pdfhttp://riull.ull.es/xmlui/handle/915/39027reponame:RIULL. Repositorio Institucional de la Universidad de La Lagunainstname:Universidad de La Laguna (ULL)InglésApplied Numerical Mathematics, Volume 188, June 2023Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ESoai:riull.ull.es:915/390272026-06-22T13:13:57Z
dc.title.none.fl_str_mv Generalized TASE-RK methods for stiff problems
title Generalized TASE-RK methods for stiff problems
spellingShingle Generalized TASE-RK methods for stiff problems
Hernández Abreu, Domingo
Explicit Runge-Kutta methods
TASE-RK methods
W-methods
Rosenbrock methods
Time Integration
Stability
Stiffness
title_short Generalized TASE-RK methods for stiff problems
title_full Generalized TASE-RK methods for stiff problems
title_fullStr Generalized TASE-RK methods for stiff problems
title_full_unstemmed Generalized TASE-RK methods for stiff problems
title_sort Generalized TASE-RK methods for stiff problems
dc.creator.none.fl_str_mv Hernández Abreu, Domingo
Gonz´alez Pinto
Pagano, G.
P´erez Rodr´ıguez, S.
author Hernández Abreu, Domingo
author_facet Hernández Abreu, Domingo
Gonz´alez Pinto
Pagano, G.
P´erez Rodr´ıguez, S.
author_role author
author2 Gonz´alez Pinto
Pagano, G.
P´erez Rodr´ıguez, S.
author2_role author
author
author
dc.contributor.none.fl_str_mv Análisis Matemático
Grupo de investigación ULL: "Métodos numéricos en ecuaciones diferenciales" https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/
dc.subject.none.fl_str_mv Explicit Runge-Kutta methods
TASE-RK methods
W-methods
Rosenbrock methods
Time Integration
Stability
Stiffness
topic Explicit Runge-Kutta methods
TASE-RK methods
W-methods
Rosenbrock methods
Time Integration
Stability
Stiffness
description A family of Time-Accurate and Stable Explicit (TASE) methods for the numerical integration of Initial Value Problems in stiff Ordinary Differential Equations (ODEs) y ′(t) = f(t, y) was recently introduced in [1]. The main idea was to make local extrapolation of a stabilized Euler method. More recently, in [3] a similar approach by considering the stabilization of arbitrary explicit Runge-Kutta methods (TASE-RK) was analyzed. In this case the explicit Runge-Kutta method integrates a transformed ODE obtained by multiplying the vector field f(t, y) by a certain operator which approximates the identity mapping up to a given order p. The main inconvenience of both approaches is that to reach order p the solution of p2 linear systems plus the evaluation of p derivatives are required per integration step. In order to substantially reduce the computational costs of the former approaches in the linear system solution, but maintaining the good accuracy and stability properties, a new family of TASE-RK methods which allow to introduce a few more free parameters are considered. The formulation of the methods was conceived to be implemented not only in sequential mode but it admits parallelism in a straigthforward way. Furthermore, since these methods are linearly implicit, connections to the class of W-methods [19] are properly established. The order conditions for the new class of methods are widely studied by using the rooted tree theory. For p = 3, 4, new methods with p sequential stages and order p are derived and compared on semidiscrete 1D and 2D Partial Differential Equations (PDEs) to those in [1, 3] and other standard Rosenbrock and W-methods in the literature.
publishDate 2023
dc.date.none.fl_str_mv 2023
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://riull.ull.es/xmlui/handle/915/39027
url http://riull.ull.es/xmlui/handle/915/39027
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Applied Numerical Mathematics, Volume 188, June 2023
dc.rights.none.fl_str_mv Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES
rights_invalid_str_mv Licencia Creative Commons (Reconocimiento-No comercial-Sin obras derivadas 4.0 Internacional)
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es_ES
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIULL. Repositorio Institucional de la Universidad de La Laguna
instname:Universidad de La Laguna (ULL)
instname_str Universidad de La Laguna (ULL)
reponame_str RIULL. Repositorio Institucional de la Universidad de La Laguna
collection RIULL. Repositorio Institucional de la Universidad de La Laguna
repository.name.fl_str_mv
repository.mail.fl_str_mv
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