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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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241650 |
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| author | Zunyuan Hu Can Li Shimin Guo |
| author_facet | Zunyuan Hu Can Li Shimin Guo |
| author_sort | Zunyuan Hu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4cb965684e8b43c1ad6b6e5d563d1c59 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-4cb965684e8b43c1ad6b6e5d563d1c592025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912346473467310.3934/math.20241650Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equationZunyuan Hu0Can Li1Shimin Guo2Department of Applied Mathematics, Xi'an University of Technology, Xi'an, Shaanxi 710054, ChinaDepartment of Applied Mathematics, Xi'an University of Technology, Xi'an, Shaanxi 710054, ChinaSchool of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/math.20241650spectral collocation methodgeneralized memory kernelsum-of-exponentialerror estimates |
| spellingShingle | Zunyuan Hu Can Li Shimin Guo Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation AIMS Mathematics spectral collocation method generalized memory kernel sum-of-exponential error estimates |
| title | Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation |
| title_full | Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation |
| title_fullStr | Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation |
| title_full_unstemmed | Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation |
| title_short | Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation |
| title_sort | fast finite difference legendre spectral collocation approximations for a tempered time fractional diffusion equation |
| topic | spectral collocation method generalized memory kernel sum-of-exponential error estimates |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241650 |
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