Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation
The present work is concerned with the efficient numerical schemes for a time-fractional diffusion equation with tempered memory kernel. The numerical schemes are established by using a $ L1 $ difference scheme for generalized Caputo fractional derivative in the temporal variable, and applying the L...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241650 |
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| Summary: | The present work is concerned with the efficient numerical schemes for a time-fractional diffusion equation with tempered memory kernel. The numerical schemes are established by using a $ L1 $ difference scheme for generalized Caputo fractional derivative in the temporal variable, and applying the Legendre spectral collocation method for the spatial variable. The sum-of-exponential technique developed in [Jiang et al., Commun. Comput. Phys., 21 (2017), 650-678] is used to discrete generalized fractional derivative with exponential kernel. The stability and convergence of the semi-discrete and fully discrete schemes are strictly proved. Some numerical examples are shown to illustrate the theoretical results and the efficiency of the present methods for two-dimensional problems. |
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| ISSN: | 2473-6988 |