Numerical solution of boundary value problems by using an optimized two-step block method.

[EN]This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. The...

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Detalles Bibliográficos
Autores: Ramos Calle, Higinio, Rufai, Mufutau Ajani
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/157032
Acceso en línea:http://hdl.handle.net/10366/157032
Access Level:acceso abierto
Palabra clave:Ordinary differential equations
Boundary value problems
Optimized hybrid block method
Homotopy-type strategy
Convergence analysis
12 Matemáticas
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spelling Numerical solution of boundary value problems by using an optimized two-step block method.Ramos Calle, HiginioRufai, Mufutau AjaniOrdinary differential equationsBoundary value problemsOptimized hybrid block methodHomotopy-type strategyConvergence analysis12 Matemáticas[EN]This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. The final approximate solution is obtained through a homotopy-type strategy which is used in order to get starting values for Newton’s method. The convergence analysis shows that the proposed method has at least fifth order of convergence. Some numerical experiments such as Bratu’s problem, singularly perturbed, and nonlinear system of BVPs are presented to illustrate the better performance of the proposed approach in comparison with other methods available in the recent literature.Springer202420242019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/157032reponame: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:10366/1570322026-06-07T06:28:51Z
dc.title.none.fl_str_mv Numerical solution of boundary value problems by using an optimized two-step block method.
title Numerical solution of boundary value problems by using an optimized two-step block method.
spellingShingle Numerical solution of boundary value problems by using an optimized two-step block method.
Ramos Calle, Higinio
Ordinary differential equations
Boundary value problems
Optimized hybrid block method
Homotopy-type strategy
Convergence analysis
12 Matemáticas
title_short Numerical solution of boundary value problems by using an optimized two-step block method.
title_full Numerical solution of boundary value problems by using an optimized two-step block method.
title_fullStr Numerical solution of boundary value problems by using an optimized two-step block method.
title_full_unstemmed Numerical solution of boundary value problems by using an optimized two-step block method.
title_sort Numerical solution of boundary value problems by using an optimized two-step block method.
dc.creator.none.fl_str_mv Ramos Calle, Higinio
Rufai, Mufutau Ajani
author Ramos Calle, Higinio
author_facet Ramos Calle, Higinio
Rufai, Mufutau Ajani
author_role author
author2 Rufai, Mufutau Ajani
author2_role author
dc.subject.none.fl_str_mv Ordinary differential equations
Boundary value problems
Optimized hybrid block method
Homotopy-type strategy
Convergence analysis
12 Matemáticas
topic Ordinary differential equations
Boundary value problems
Optimized hybrid block method
Homotopy-type strategy
Convergence analysis
12 Matemáticas
description [EN]This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. The final approximate solution is obtained through a homotopy-type strategy which is used in order to get starting values for Newton’s method. The convergence analysis shows that the proposed method has at least fifth order of convergence. Some numerical experiments such as Bratu’s problem, singularly perturbed, and nonlinear system of BVPs are presented to illustrate the better performance of the proposed approach in comparison with other methods available in the recent literature.
publishDate 2019
dc.date.none.fl_str_mv 2019
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/10366/157032
url http://hdl.handle.net/10366/157032
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 Springer
publisher.none.fl_str_mv Springer
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
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score 15,300724

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