Convergence of Finite Difference Method in Positive Time for Multi-Term Time Fractional Differential Equations
Year: 2020
Author: Haili Qiao, Aijie Cheng
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 774–785
Abstract
A multi-time fractional-order reaction-diffusion equation with the Caputo fractional derivative is considered. On a uniform grid, the problem is discretised by using the $L$1 formula. For the problem solutions with a singularity at time $t$ = 0, the convergence order is $\mathcal{O}(τ^{α_1})$. For any subdomain bounded away from $t$ = 0, the method has the convergence rate $\mathcal{O}(τ)$, which is better than the convergence rate $\mathcal{O}(τ^{α_1})$ for the whole time-space domain. Results of theoretical analysis are illustrated by numerical experiments.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.040220.020520
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 774–785
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Caputo fractional derivative multi-term fractional differential equation weak singularity uniform mesh L1 scheme.