Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative
In this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, a special discrete scheme of C-F derivative is used in time direction and a compact difference operator is used in space direction. Second, we discuss the co...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/7906656 |
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| _version_ | 1832548013064585216 |
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| author | Hanxiao Wang Xindong Zhang Ziyang Luo Juan Liu |
| author_facet | Hanxiao Wang Xindong Zhang Ziyang Luo Juan Liu |
| author_sort | Hanxiao Wang |
| collection | DOAJ |
| description | In this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, a special discrete scheme of C-F derivative is used in time direction and a compact difference operator is used in space direction. Second, we discuss the convergence of the proposed method in discrete L1-norm and L2-norm. The convergence order of our discrete scheme is Oτ2+h4, where τ and h are the temporal and spatial step sizes, respectively. The aim of this paper is to show that fractional operator without singular term is very useful for improving the accuracy of discrete scheme. |
| format | Article |
| id | doaj-art-c86482b3919e4ee8a7e74fe3ba92d9c4 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c86482b3919e4ee8a7e74fe3ba92d9c42025-02-03T06:42:43ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/7906656Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio DerivativeHanxiao Wang0Xindong Zhang1Ziyang Luo2Juan Liu3School of Mathematical SciencesSchool of Mathematical SciencesSchool of Mathematical SciencesCollege of Big Data StatisticsIn this paper, we propose a high-precision discrete scheme for the time-fractional diffusion equation (TFDE) with Caputo-Fabrizio type. First, a special discrete scheme of C-F derivative is used in time direction and a compact difference operator is used in space direction. Second, we discuss the convergence of the proposed method in discrete L1-norm and L2-norm. The convergence order of our discrete scheme is Oτ2+h4, where τ and h are the temporal and spatial step sizes, respectively. The aim of this paper is to show that fractional operator without singular term is very useful for improving the accuracy of discrete scheme.http://dx.doi.org/10.1155/2023/7906656 |
| spellingShingle | Hanxiao Wang Xindong Zhang Ziyang Luo Juan Liu Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative Journal of Mathematics |
| title | Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative |
| title_full | Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative |
| title_fullStr | Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative |
| title_full_unstemmed | Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative |
| title_short | Analysis of Numerical Method for Diffusion Equation with Time-Fractional Caputo–Fabrizio Derivative |
| title_sort | analysis of numerical method for diffusion equation with time fractional caputo fabrizio derivative |
| url | http://dx.doi.org/10.1155/2023/7906656 |
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