A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations
Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jac...
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| Autor*in: |
Hafez, Ramy M. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 82(2015), 3 vom: 12. Juli, Seite 1431-1440 |
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| Übergeordnetes Werk: |
volume:82 ; year:2015 ; number:3 ; day:12 ; month:07 ; pages:1431-1440 |
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| DOI / URN: |
10.1007/s11071-015-2250-7 |
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OLC2051112045 |
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| 520 | |a Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. | ||
| 650 | 4 | |a Collocation method | |
| 650 | 4 | |a Jacobi polynomials | |
| 650 | 4 | |a Gauss–Lobatto quadrature | |
| 650 | 4 | |a Gauss–Radau quadrature | |
| 650 | 4 | |a Fractional Fokker–Planck equation | |
| 650 | 4 | |a Caputo fractional derivatives | |
| 700 | 1 | |a Ezz-Eldien, Samer S. |4 aut | |
| 700 | 1 | |a Bhrawy, Ali H. |4 aut | |
| 700 | 1 | |a Ahmed, Engy A. |4 aut | |
| 700 | 1 | |a Baleanu, Dumitru |4 aut | |
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10.1007/s11071-015-2250-7 doi (DE-627)OLC2051112045 (DE-He213)s11071-015-2250-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Hafez, Ramy M. verfasserin aut A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2015 Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. Collocation method Jacobi polynomials Gauss–Lobatto quadrature Gauss–Radau quadrature Fractional Fokker–Planck equation Caputo fractional derivatives Ezz-Eldien, Samer S. aut Bhrawy, Ali H. aut Ahmed, Engy A. aut Baleanu, Dumitru aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 82(2015), 3 vom: 12. Juli, Seite 1431-1440 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:82 year:2015 number:3 day:12 month:07 pages:1431-1440 https://doi.org/10.1007/s11071-015-2250-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 82 2015 3 12 07 1431-1440 |
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10.1007/s11071-015-2250-7 doi (DE-627)OLC2051112045 (DE-He213)s11071-015-2250-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Hafez, Ramy M. verfasserin aut A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2015 Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. Collocation method Jacobi polynomials Gauss–Lobatto quadrature Gauss–Radau quadrature Fractional Fokker–Planck equation Caputo fractional derivatives Ezz-Eldien, Samer S. aut Bhrawy, Ali H. aut Ahmed, Engy A. aut Baleanu, Dumitru aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 82(2015), 3 vom: 12. Juli, Seite 1431-1440 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:82 year:2015 number:3 day:12 month:07 pages:1431-1440 https://doi.org/10.1007/s11071-015-2250-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 82 2015 3 12 07 1431-1440 |
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10.1007/s11071-015-2250-7 doi (DE-627)OLC2051112045 (DE-He213)s11071-015-2250-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Hafez, Ramy M. verfasserin aut A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2015 Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. Collocation method Jacobi polynomials Gauss–Lobatto quadrature Gauss–Radau quadrature Fractional Fokker–Planck equation Caputo fractional derivatives Ezz-Eldien, Samer S. aut Bhrawy, Ali H. aut Ahmed, Engy A. aut Baleanu, Dumitru aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 82(2015), 3 vom: 12. Juli, Seite 1431-1440 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:82 year:2015 number:3 day:12 month:07 pages:1431-1440 https://doi.org/10.1007/s11071-015-2250-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 82 2015 3 12 07 1431-1440 |
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10.1007/s11071-015-2250-7 doi (DE-627)OLC2051112045 (DE-He213)s11071-015-2250-7-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Hafez, Ramy M. verfasserin aut A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2015 Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. Collocation method Jacobi polynomials Gauss–Lobatto quadrature Gauss–Radau quadrature Fractional Fokker–Planck equation Caputo fractional derivatives Ezz-Eldien, Samer S. aut Bhrawy, Ali H. aut Ahmed, Engy A. aut Baleanu, Dumitru aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 82(2015), 3 vom: 12. Juli, Seite 1431-1440 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:82 year:2015 number:3 day:12 month:07 pages:1431-1440 https://doi.org/10.1007/s11071-015-2250-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 82 2015 3 12 07 1431-1440 |
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a jacobi gauss–lobatto and gauss–radau collocation algorithm for solving fractional fokker–planck equations |
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A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations |
| abstract |
Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. © Springer Science+Business Media Dordrecht 2015 |
| abstractGer |
Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. © Springer Science+Business Media Dordrecht 2015 |
| abstract_unstemmed |
Abstract In this article, we construct a new numerical approach for solving the time-fractional Fokker–Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss–Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss–Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker–Planck equation and the time–space-fractional Fokker–Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm. © Springer Science+Business Media Dordrecht 2015 |
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| title_short |
A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations |
| url |
https://doi.org/10.1007/s11071-015-2250-7 |
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| author2 |
Ezz-Eldien, Samer S. Bhrawy, Ali H. Ahmed, Engy A. Baleanu, Dumitru |
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Ezz-Eldien, Samer S. Bhrawy, Ali H. Ahmed, Engy A. Baleanu, Dumitru |
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130936782 |
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| doi_str |
10.1007/s11071-015-2250-7 |
| up_date |
2024-07-04T03:36:33.851Z |
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