Linear B-spline finite element method for the generalized diffusion equation with delay

OBJECTIVES: The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of...

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Detalles Bibliográficos
Autores principales: Lubo, Gemeda Tolessa, Duressa, Gemechis File
Formato: Online Artículo Texto
Lenguaje:English
Publicado: BioMed Central 2022
Materias:
Research Note
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9166504/
https://www.ncbi.nlm.nih.gov/pubmed/35658930
http://dx.doi.org/10.1186/s13104-022-06078-0
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author Lubo, Gemeda Tolessa
Duressa, Gemechis File
author_facet Lubo, Gemeda Tolessa
Duressa, Gemechis File
author_sort Lubo, Gemeda Tolessa
collection PubMed
description OBJECTIVES: The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that the numerical solution is obtained as a smooth piecewise continuous function which empowers one to find an approximate solution at any desired position in the domain. RESULT: Sufficient and necessary conditions for the numerical method to be asymptotically stable are derived. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method.
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spelling pubmed-91665042022-06-05 Linear B-spline finite element method for the generalized diffusion equation with delay Lubo, Gemeda Tolessa Duressa, Gemechis File BMC Res Notes Research Note OBJECTIVES: The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that the numerical solution is obtained as a smooth piecewise continuous function which empowers one to find an approximate solution at any desired position in the domain. RESULT: Sufficient and necessary conditions for the numerical method to be asymptotically stable are derived. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method. BioMed Central 2022-06-03 /pmc/articles/PMC9166504/ /pubmed/35658930 http://dx.doi.org/10.1186/s13104-022-06078-0 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/ (https://creativecommons.org/publicdomain/zero/1.0/) ) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
spellingShingle Research Note
Lubo, Gemeda Tolessa
Duressa, Gemechis File
Linear B-spline finite element method for the generalized diffusion equation with delay
title Linear B-spline finite element method for the generalized diffusion equation with delay
title_full Linear B-spline finite element method for the generalized diffusion equation with delay
title_fullStr Linear B-spline finite element method for the generalized diffusion equation with delay
title_full_unstemmed Linear B-spline finite element method for the generalized diffusion equation with delay
title_short Linear B-spline finite element method for the generalized diffusion equation with delay
title_sort linear b-spline finite element method for the generalized diffusion equation with delay
topic Research Note
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9166504/
https://www.ncbi.nlm.nih.gov/pubmed/35658930
http://dx.doi.org/10.1186/s13104-022-06078-0
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