Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time
Year: 2018
Author: Jin-Ye Shen, Zhi-Zhong Sun, Rui Du
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 834–858
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.010418.020718
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 834–858
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Fractional differential equation difference scheme fast algorithm singularity.