A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.

[EN]In this paper, an efficient fourth-derivative two-step hybrid block strategy (FDTHBS) to get the approximate solution of a third-order IVP with applications to problems in Fluid Dynamics and Engineering is constructed. The mathematical derivation of the proposed FDTHBS is based on the interpolat...

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Detalles Bibliográficos
Autores: Rufai, Mufutau Ajani, Ramos Calle, Higinio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/156707
Acceso en línea:http://hdl.handle.net/10366/156707
Access Level:acceso abierto
Palabra clave:Ordinary differential equations
Third-order initial value problems
Variable step-size formulation
Fourth-derivative hybrid block method
Collocation and interpolation techniques
12 Matemáticas
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spelling A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.Rufai, Mufutau AjaniRamos Calle, HiginioOrdinary differential equationsThird-order initial value problemsVariable step-size formulationFourth-derivative hybrid block methodCollocation and interpolation techniques12 Matemáticas[EN]In this paper, an efficient fourth-derivative two-step hybrid block strategy (FDTHBS) to get the approximate solution of a third-order IVP with applications to problems in Fluid Dynamics and Engineering is constructed. The mathematical derivation of the proposed FDTHBS is based on the interpolation and collocation of the exact solution and its derivatives at the selected equidistant grid and off-grid points. The theoretical characteristics of the proposed method are analysed. An embedding-like procedure is considered and executed in variable step-size mode to get better performance of the newly developed strategy. Some test problems, including the well-known Blasius equation and three different types of non-linear thin-film flow problems, are integrated numerically to ascertain the superior impact of our developed error estimation and control strategy. It is worth concluding that the proposed technique is not only efficient in term of CPU time, but also minimizes errors and support the analytical results.Taylor and Francis202420242021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/156707reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1567072026-06-07T06:28:51Z
dc.title.none.fl_str_mv A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
title A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
spellingShingle A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
Rufai, Mufutau Ajani
Ordinary differential equations
Third-order initial value problems
Variable step-size formulation
Fourth-derivative hybrid block method
Collocation and interpolation techniques
12 Matemáticas
title_short A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
title_full A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
title_fullStr A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
title_full_unstemmed A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
title_sort A variable step-size fourth-derivative hybrid block strategy for integrating third-order IVPs, with applications.
dc.creator.none.fl_str_mv Rufai, Mufutau Ajani
Ramos Calle, Higinio
author Rufai, Mufutau Ajani
author_facet Rufai, Mufutau Ajani
Ramos Calle, Higinio
author_role author
author2 Ramos Calle, Higinio
author2_role author
dc.subject.none.fl_str_mv Ordinary differential equations
Third-order initial value problems
Variable step-size formulation
Fourth-derivative hybrid block method
Collocation and interpolation techniques
12 Matemáticas
topic Ordinary differential equations
Third-order initial value problems
Variable step-size formulation
Fourth-derivative hybrid block method
Collocation and interpolation techniques
12 Matemáticas
description [EN]In this paper, an efficient fourth-derivative two-step hybrid block strategy (FDTHBS) to get the approximate solution of a third-order IVP with applications to problems in Fluid Dynamics and Engineering is constructed. The mathematical derivation of the proposed FDTHBS is based on the interpolation and collocation of the exact solution and its derivatives at the selected equidistant grid and off-grid points. The theoretical characteristics of the proposed method are analysed. An embedding-like procedure is considered and executed in variable step-size mode to get better performance of the newly developed strategy. Some test problems, including the well-known Blasius equation and three different types of non-linear thin-film flow problems, are integrated numerically to ascertain the superior impact of our developed error estimation and control strategy. It is worth concluding that the proposed technique is not only efficient in term of CPU time, but also minimizes errors and support the analytical results.
publishDate 2021
dc.date.none.fl_str_mv 2021
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/156707
url http://hdl.handle.net/10366/156707
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Taylor and Francis
publisher.none.fl_str_mv Taylor and Francis
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869413435144404992
score 15.300724

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