Accurate numerical scheme for singularly perturbed parabolic delay differential equation

OBJECTIVES: Numerical treatment of singularly perturbed parabolic delay differential equation is considered. Solution of the equation exhibits a boundary layer, which makes it difficult for numerical computation. Accurate numerical scheme is proposed using [Formula: see text] -method in time discret...

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Autores principales: Woldaregay, Mesfin Mekuria, Duressa, Gemechis File
Formato: Online Artículo Texto
Lenguaje:English
Publicado: BioMed Central 2021
Materias:
Research Note
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8444430/
https://www.ncbi.nlm.nih.gov/pubmed/34526134
http://dx.doi.org/10.1186/s13104-021-05769-4
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author Woldaregay, Mesfin Mekuria
Duressa, Gemechis File
author_facet Woldaregay, Mesfin Mekuria
Duressa, Gemechis File
author_sort Woldaregay, Mesfin Mekuria
collection PubMed
description OBJECTIVES: Numerical treatment of singularly perturbed parabolic delay differential equation is considered. Solution of the equation exhibits a boundary layer, which makes it difficult for numerical computation. Accurate numerical scheme is proposed using [Formula: see text] -method in time discretization and non-standard finite difference method in space discretization. RESULT: Stability and uniform convergence of the proposed scheme is investigated. The scheme is uniformly convergent with linear order of convergence before Richardson extrapolation and second order convergent after Richardson extrapolation. Numerical examples are considered to validate the theoretical findings.
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spelling pubmed-84444302021-09-16 Accurate numerical scheme for singularly perturbed parabolic delay differential equation Woldaregay, Mesfin Mekuria Duressa, Gemechis File BMC Res Notes Research Note OBJECTIVES: Numerical treatment of singularly perturbed parabolic delay differential equation is considered. Solution of the equation exhibits a boundary layer, which makes it difficult for numerical computation. Accurate numerical scheme is proposed using [Formula: see text] -method in time discretization and non-standard finite difference method in space discretization. RESULT: Stability and uniform convergence of the proposed scheme is investigated. The scheme is uniformly convergent with linear order of convergence before Richardson extrapolation and second order convergent after Richardson extrapolation. Numerical examples are considered to validate the theoretical findings. BioMed Central 2021-09-15 /pmc/articles/PMC8444430/ /pubmed/34526134 http://dx.doi.org/10.1186/s13104-021-05769-4 Text en © The Author(s) 2021 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
Woldaregay, Mesfin Mekuria
Duressa, Gemechis File
Accurate numerical scheme for singularly perturbed parabolic delay differential equation
title Accurate numerical scheme for singularly perturbed parabolic delay differential equation
title_full Accurate numerical scheme for singularly perturbed parabolic delay differential equation
title_fullStr Accurate numerical scheme for singularly perturbed parabolic delay differential equation
title_full_unstemmed Accurate numerical scheme for singularly perturbed parabolic delay differential equation
title_short Accurate numerical scheme for singularly perturbed parabolic delay differential equation
title_sort accurate numerical scheme for singularly perturbed parabolic delay differential equation
topic Research Note
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8444430/
https://www.ncbi.nlm.nih.gov/pubmed/34526134
http://dx.doi.org/10.1186/s13104-021-05769-4
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