Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay
A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method, and extrapolation methods in the temporal direction....
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9981211 |
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| _version_ | 1850171554884747264 |
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| author | Lili Li Mianfu She Yuanling Niu |
| author_facet | Lili Li Mianfu She Yuanling Niu |
| author_sort | Lili Li |
| collection | DOAJ |
| description | A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method, and extrapolation methods in the temporal direction. A novel discrete fractional Grönwall inequality is established. Thanks to the inequality, the error estimate of a fully discrete scheme is obtained. Several numerical examples are provided to verify the effectiveness of the fully discrete numerical method. |
| format | Article |
| id | doaj-art-9a1a44e474b44e2eaaf6f49a6020dc10 |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9a1a44e474b44e2eaaf6f49a6020dc102025-08-20T02:20:16ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/99812119981211Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time DelayLili Li0Mianfu She1Yuanling Niu2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaA linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method, and extrapolation methods in the temporal direction. A novel discrete fractional Grönwall inequality is established. Thanks to the inequality, the error estimate of a fully discrete scheme is obtained. Several numerical examples are provided to verify the effectiveness of the fully discrete numerical method.http://dx.doi.org/10.1155/2021/9981211 |
| spellingShingle | Lili Li Mianfu She Yuanling Niu Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay Journal of Function Spaces |
| title | Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay |
| title_full | Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay |
| title_fullStr | Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay |
| title_full_unstemmed | Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay |
| title_short | Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay |
| title_sort | fractional crank nicolson galerkin finite element methods for nonlinear time fractional parabolic problems with time delay |
| url | http://dx.doi.org/10.1155/2021/9981211 |
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