@article{Hu2024, 
author = {Zunyuan Hu and Can Li and Shimin Guo},
title = {Fast finite difference/Legendre spectral collocation approximations for a tempered time-fractional diffusion equation},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {34647-34673},
keywords = {spectral collocation method, generalized memory kernel, sum-of-exponential, error estimates},
url = {https://www.sciopen.com/article/10.3934/math.20241650},
doi = {10.3934/math.20241650},
abstract = {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.}
}