East Asian J. Appl. Math., 10 (2020), pp. 774-785.
Published online: 2020-08
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.040220.020520}, url = {http://global-sci.org/intro/article_detail/eajam/17960.html} }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.