$Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination$
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Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional...

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Autores principales:	Hadhoud Adel R., Abd Alaal Faisal E., Abdelaziz Ayman A., Radwan Taha
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	the generalized time-fractional huxley-burgers’ equation the mean value theorem the cubic b-spline collocation method stability analysis 34dxx 35r11 65-xx 65d07 65l60 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/58db07bd0507478b827802a03388d735
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spelling	oai:doaj.org-article:58db07bd0507478b827802a03388d7352021-12-05T14:10:45ZNumerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination2391-466110.1515/dema-2021-0040https://doaj.org/article/58db07bd0507478b827802a03388d7352021-11-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0040https://doaj.org/toc/2391-4661In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.Hadhoud Adel R.Abd Alaal Faisal E.Abdelaziz Ayman A.Radwan TahaDe Gruyterarticlethe generalized time-fractional huxley-burgers’ equationthe mean value theoremthe cubic b-splinecollocation methodstability analysis34dxx35r1165-xx65d0765l60MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 436-451 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	the generalized time-fractional huxley-burgers’ equation the mean value theorem the cubic b-spline collocation method stability analysis 34dxx 35r11 65-xx 65d07 65l60 Mathematics QA1-939
spellingShingle	the generalized time-fractional huxley-burgers’ equation the mean value theorem the cubic b-spline collocation method stability analysis 34dxx 35r11 65-xx 65d07 65l60 Mathematics QA1-939 Hadhoud Adel R. Abd Alaal Faisal E. Abdelaziz Ayman A. Radwan Taha Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
description	In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.
format	article
author	Hadhoud Adel R. Abd Alaal Faisal E. Abdelaziz Ayman A. Radwan Taha
author_facet	Hadhoud Adel R. Abd Alaal Faisal E. Abdelaziz Ayman A. Radwan Taha
author_sort	Hadhoud Adel R.
title	Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
title_short	Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
title_full	Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
title_fullStr	Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
title_full_unstemmed	Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
title_sort	numerical treatment of the generalized time-fractional huxley-burgers’ equation and its stability examination
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/58db07bd0507478b827802a03388d735
work_keys_str_mv	AT hadhoudadelr numericaltreatmentofthegeneralizedtimefractionalhuxleyburgersequationanditsstabilityexamination AT abdalaalfaisale numericaltreatmentofthegeneralizedtimefractionalhuxleyburgersequationanditsstabilityexamination AT abdelazizaymana numericaltreatmentofthegeneralizedtimefractionalhuxleyburgersequationanditsstabilityexamination AT radwantaha numericaltreatmentofthegeneralizedtimefractionalhuxleyburgersequationanditsstabilityexamination
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Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

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