@Article{EAJAM-8-4,
author = {Shen, Jin-Ye and Zhi-Zhong, Sun and Rui, Du},
title = {Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {8},
number = {4},
pages = {834--858},
abstract = {<p style="text-align: justify;">A sharp estimate for the L1 formula on graded meshes, which approximates
the Caputo derivatives of functions with a weak singularity at t = 0 is obtained. Combining
such approximations with the sum-of-exponential approximations of the kernel, we
develop fast difference schemes for one- and two-dimensional fractional diffusion equations,
the solutions of which have a weak singularity at the starting time. The proof of
the stability and convergence is based on the maximum principle. Numerical examples
confirm theoretical estimates.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.010418.020718},
url = {https://global-sci.com/article/82682/fast-finite-difference-schemes-for-time-fractional-diffusion-equations-with-a-weak-singularity-at-initial-time}
}