Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations

OBJECTIVE: The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. RESULTS: The quasilinearization technique is used to linearize the nonlinear term. A no...

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Detalles Bibliográficos
Autores principales: Kabeto, Masho Jima, 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/PMC8666058/
https://www.ncbi.nlm.nih.gov/pubmed/34895302
http://dx.doi.org/10.1186/s13104-021-05858-4
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author Kabeto, Masho Jima
Duressa, Gemechis File
author_facet Kabeto, Masho Jima
Duressa, Gemechis File
author_sort Kabeto, Masho Jima
collection PubMed
description OBJECTIVE: The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. RESULTS: The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results.
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spelling pubmed-86660582021-12-13 Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations Kabeto, Masho Jima Duressa, Gemechis File BMC Res Notes Research Note OBJECTIVE: The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. RESULTS: The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results. BioMed Central 2021-12-11 /pmc/articles/PMC8666058/ /pubmed/34895302 http://dx.doi.org/10.1186/s13104-021-05858-4 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
Kabeto, Masho Jima
Duressa, Gemechis File
Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
title Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
title_full Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
title_fullStr Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
title_full_unstemmed Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
title_short Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations
title_sort accelerated nonstandard finite difference method for singularly perturbed burger-huxley equations
topic Research Note
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8666058/
https://www.ncbi.nlm.nih.gov/pubmed/34895302
http://dx.doi.org/10.1186/s13104-021-05858-4
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