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 -

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.