A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation

The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines...
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Autor*in:	Xiao Qin [verfasserIn] Xiaozhong Yang [verfasserIn] Peng Lyu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	generalized time fractional fisher equation explicit implicit alternating difference scheme stability convergence numerical experiments

Übergeordnetes Werk:	In: AIMS Mathematics - AIMS Press, 2018, 6(2021), 10, Seite 11449-11466
Übergeordnetes Werk:	volume:6 ; year:2021 ; number:10 ; pages:11449-11466

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3934/math.2021663

Katalog-ID:	DOAJ051577682

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520			\|a The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation.
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spelling	10.3934/math.2021663 doi (DE-627)DOAJ051577682 (DE-599)DOAJ77bddbf525864d64b107b3eb47c2b6fe DE-627 ger DE-627 rakwb eng QA1-939 Xiao Qin verfasserin aut A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation. generalized time fractional fisher equation explicit implicit alternating difference scheme stability convergence numerical experiments Mathematics Xiaozhong Yang verfasserin aut Peng Lyu verfasserin aut In AIMS Mathematics AIMS Press, 2018 6(2021), 10, Seite 11449-11466 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:6 year:2021 number:10 pages:11449-11466 https://doi.org/10.3934/math.2021663 kostenfrei https://doaj.org/article/77bddbf525864d64b107b3eb47c2b6fe kostenfrei https://www.aimspress.com/article/doi/10.3934/math.2021663?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2021 10 11449-11466
allfields_unstemmed	10.3934/math.2021663 doi (DE-627)DOAJ051577682 (DE-599)DOAJ77bddbf525864d64b107b3eb47c2b6fe DE-627 ger DE-627 rakwb eng QA1-939 Xiao Qin verfasserin aut A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation. generalized time fractional fisher equation explicit implicit alternating difference scheme stability convergence numerical experiments Mathematics Xiaozhong Yang verfasserin aut Peng Lyu verfasserin aut In AIMS Mathematics AIMS Press, 2018 6(2021), 10, Seite 11449-11466 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:6 year:2021 number:10 pages:11449-11466 https://doi.org/10.3934/math.2021663 kostenfrei https://doaj.org/article/77bddbf525864d64b107b3eb47c2b6fe kostenfrei https://www.aimspress.com/article/doi/10.3934/math.2021663?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2021 10 11449-11466
allfieldsGer	10.3934/math.2021663 doi (DE-627)DOAJ051577682 (DE-599)DOAJ77bddbf525864d64b107b3eb47c2b6fe DE-627 ger DE-627 rakwb eng QA1-939 Xiao Qin verfasserin aut A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation. generalized time fractional fisher equation explicit implicit alternating difference scheme stability convergence numerical experiments Mathematics Xiaozhong Yang verfasserin aut Peng Lyu verfasserin aut In AIMS Mathematics AIMS Press, 2018 6(2021), 10, Seite 11449-11466 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:6 year:2021 number:10 pages:11449-11466 https://doi.org/10.3934/math.2021663 kostenfrei https://doaj.org/article/77bddbf525864d64b107b3eb47c2b6fe kostenfrei https://www.aimspress.com/article/doi/10.3934/math.2021663?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2021 10 11449-11466
allfieldsSound	10.3934/math.2021663 doi (DE-627)DOAJ051577682 (DE-599)DOAJ77bddbf525864d64b107b3eb47c2b6fe DE-627 ger DE-627 rakwb eng QA1-939 Xiao Qin verfasserin aut A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation. generalized time fractional fisher equation explicit implicit alternating difference scheme stability convergence numerical experiments Mathematics Xiaozhong Yang verfasserin aut Peng Lyu verfasserin aut In AIMS Mathematics AIMS Press, 2018 6(2021), 10, Seite 11449-11466 (DE-627)1011276194 (DE-600)2917342-5 24736988 nnns volume:6 year:2021 number:10 pages:11449-11466 https://doi.org/10.3934/math.2021663 kostenfrei https://doaj.org/article/77bddbf525864d64b107b3eb47c2b6fe kostenfrei https://www.aimspress.com/article/doi/10.3934/math.2021663?viewType=HTML kostenfrei https://doaj.org/toc/2473-6988 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 6 2021 10 11449-11466
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The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. 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callnumber-first	Q - Science
author	Xiao Qin
spellingShingle	Xiao Qin misc QA1-939 misc generalized time fractional fisher equation misc explicit implicit alternating difference scheme misc stability misc convergence misc numerical experiments misc Mathematics A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation
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topic_title	QA1-939 A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation generalized time fractional fisher equation explicit implicit alternating difference scheme stability convergence numerical experiments
topic	misc QA1-939 misc generalized time fractional fisher equation misc explicit implicit alternating difference scheme misc stability misc convergence misc numerical experiments misc Mathematics
topic_unstemmed	misc QA1-939 misc generalized time fractional fisher equation misc explicit implicit alternating difference scheme misc stability misc convergence misc numerical experiments misc Mathematics
topic_browse	misc QA1-939 misc generalized time fractional fisher equation misc explicit implicit alternating difference scheme misc stability misc convergence misc numerical experiments misc Mathematics
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title	A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation
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title_full	A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation
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title_sort	class of explicit implicit alternating difference schemes for generalized time fractional fisher equation
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title_auth	A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation
abstract	The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation.
abstractGer	The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation.
abstract_unstemmed	The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation.
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title_short	A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation
url	https://doi.org/10.3934/math.2021663 https://doaj.org/article/77bddbf525864d64b107b3eb47c2b6fe https://www.aimspress.com/article/doi/10.3934/math.2021663?viewType=HTML https://doaj.org/toc/2473-6988
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A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation

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