A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution
This paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is discretized using the Crank–Nicolson formula on uniform meshe...
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MDPI AG
2025-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/4/204 |
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| author | Haili Qiao Aijie Cheng |
| author_facet | Haili Qiao Aijie Cheng |
| author_sort | Haili Qiao |
| collection | DOAJ |
| description | This paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is discretized using the Crank–Nicolson formula on uniform meshes, and a local truncation error estimate is provided. The spatial derivative is discretized using the central difference quotient on uniform meshes. Then, energy analysis methods are utilized to provide an optimal error estimates. On the other hand, the numerical scheme is optimized based on the sum-of-exponentials approximation, effectively reducing computation and memory requirements. Finally, numerical examples are simulated to verify the effectiveness of the algorithm. |
| format | Article |
| id | doaj-art-3da741be83894ef391ba65a73ccd498c |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-3da741be83894ef391ba65a73ccd498c2025-08-20T02:28:28ZengMDPI AGFractal and Fractional2504-31102025-03-019420410.3390/fractalfract9040204A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular SolutionHaili Qiao0Aijie Cheng1School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaThis paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is discretized using the Crank–Nicolson formula on uniform meshes, and a local truncation error estimate is provided. The spatial derivative is discretized using the central difference quotient on uniform meshes. Then, energy analysis methods are utilized to provide an optimal error estimates. On the other hand, the numerical scheme is optimized based on the sum-of-exponentials approximation, effectively reducing computation and memory requirements. Finally, numerical examples are simulated to verify the effectiveness of the algorithm.https://www.mdpi.com/2504-3110/9/4/2042D time fractional mobile/immobile equationweak singularityCrank–Nicolson L1 formulaerror estimatessum-of-exponentials approximation |
| spellingShingle | Haili Qiao Aijie Cheng A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution Fractal and Fractional 2D time fractional mobile/immobile equation weak singularity Crank–Nicolson L1 formula error estimates sum-of-exponentials approximation |
| title | A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution |
| title_full | A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution |
| title_fullStr | A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution |
| title_full_unstemmed | A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution |
| title_short | A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution |
| title_sort | fast finite difference method for 2d time fractional mobile immobile equation with weakly singular solution |
| topic | 2D time fractional mobile/immobile equation weak singularity Crank–Nicolson L1 formula error estimates sum-of-exponentials approximation |
| url | https://www.mdpi.com/2504-3110/9/4/204 |
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