TY - JOUR
T1 - Convergence of Finite Difference Method in Positive Time for Multi-Term Time Fractional Differential Equations
AU - Qiao , Haili
AU - Cheng , Aijie
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 774
EP - 785
PY - 2020
DA - 2020/08
SN - 10
DO - http://doi.org/10.4208/eajam.040220.020520
UR - https://global-sci.org/intro/article_detail/eajam/17960.html
KW - Caputo fractional derivative, multi-term fractional differential equation, weak singularity, uniform mesh, L1 scheme.
AB - <p style="text-align: justify;">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.</p>