A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system
Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discre...
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| Autor*in: |
Liu, Xiaoting [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Computational mechanics - Springer Berlin Heidelberg, 1986, 69(2021), 1 vom: 11. Okt., Seite 113-131 |
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volume:69 ; year:2021 ; number:1 ; day:11 ; month:10 ; pages:113-131 |
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10.1007/s00466-021-02085-3 |
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| 520 | |a Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. | ||
| 650 | 4 | |a Unsteady flow field | |
| 650 | 4 | |a Impulsive fractional-order system | |
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| 650 | 4 | |a Computational efficiency | |
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| 700 | 1 | |a Sun, HongGuang |4 aut | |
| 700 | 1 | |a Guo, Zhilin |4 aut | |
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10.1007/s00466-021-02085-3 doi (DE-627)OLC2077927739 (DE-He213)s00466-021-02085-3-p DE-627 ger DE-627 rakwb eng 530 004 VZ 11 ssgn Liu, Xiaoting verfasserin aut A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. Unsteady flow field Impulsive fractional-order system Double-scale-dependent mesh Graded mesh Computational efficiency Zhang, Yong aut Sun, HongGuang aut Guo, Zhilin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 69(2021), 1 vom: 11. Okt., Seite 113-131 (DE-627)130635170 (DE-600)799787-5 (DE-576)016140648 0178-7675 nnns volume:69 year:2021 number:1 day:11 month:10 pages:113-131 https://doi.org/10.1007/s00466-021-02085-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 69 2021 1 11 10 113-131 |
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10.1007/s00466-021-02085-3 doi (DE-627)OLC2077927739 (DE-He213)s00466-021-02085-3-p DE-627 ger DE-627 rakwb eng 530 004 VZ 11 ssgn Liu, Xiaoting verfasserin aut A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. Unsteady flow field Impulsive fractional-order system Double-scale-dependent mesh Graded mesh Computational efficiency Zhang, Yong aut Sun, HongGuang aut Guo, Zhilin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 69(2021), 1 vom: 11. Okt., Seite 113-131 (DE-627)130635170 (DE-600)799787-5 (DE-576)016140648 0178-7675 nnns volume:69 year:2021 number:1 day:11 month:10 pages:113-131 https://doi.org/10.1007/s00466-021-02085-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 69 2021 1 11 10 113-131 |
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10.1007/s00466-021-02085-3 doi (DE-627)OLC2077927739 (DE-He213)s00466-021-02085-3-p DE-627 ger DE-627 rakwb eng 530 004 VZ 11 ssgn Liu, Xiaoting verfasserin aut A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. Unsteady flow field Impulsive fractional-order system Double-scale-dependent mesh Graded mesh Computational efficiency Zhang, Yong aut Sun, HongGuang aut Guo, Zhilin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 69(2021), 1 vom: 11. Okt., Seite 113-131 (DE-627)130635170 (DE-600)799787-5 (DE-576)016140648 0178-7675 nnns volume:69 year:2021 number:1 day:11 month:10 pages:113-131 https://doi.org/10.1007/s00466-021-02085-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 69 2021 1 11 10 113-131 |
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10.1007/s00466-021-02085-3 doi (DE-627)OLC2077927739 (DE-He213)s00466-021-02085-3-p DE-627 ger DE-627 rakwb eng 530 004 VZ 11 ssgn Liu, Xiaoting verfasserin aut A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. Unsteady flow field Impulsive fractional-order system Double-scale-dependent mesh Graded mesh Computational efficiency Zhang, Yong aut Sun, HongGuang aut Guo, Zhilin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 69(2021), 1 vom: 11. Okt., Seite 113-131 (DE-627)130635170 (DE-600)799787-5 (DE-576)016140648 0178-7675 nnns volume:69 year:2021 number:1 day:11 month:10 pages:113-131 https://doi.org/10.1007/s00466-021-02085-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 69 2021 1 11 10 113-131 |
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10.1007/s00466-021-02085-3 doi (DE-627)OLC2077927739 (DE-He213)s00466-021-02085-3-p DE-627 ger DE-627 rakwb eng 530 004 VZ 11 ssgn Liu, Xiaoting verfasserin aut A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. Unsteady flow field Impulsive fractional-order system Double-scale-dependent mesh Graded mesh Computational efficiency Zhang, Yong aut Sun, HongGuang aut Guo, Zhilin aut Enthalten in Computational mechanics Springer Berlin Heidelberg, 1986 69(2021), 1 vom: 11. Okt., Seite 113-131 (DE-627)130635170 (DE-600)799787-5 (DE-576)016140648 0178-7675 nnns volume:69 year:2021 number:1 day:11 month:10 pages:113-131 https://doi.org/10.1007/s00466-021-02085-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 69 2021 1 11 10 113-131 |
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A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system |
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Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 |
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A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system |
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Zhang, Yong Sun, HongGuang Guo, Zhilin |
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