TY - JOUR
T1 - Finite Difference Methods for Fractional Differential Equations on Non-Uniform Meshes
AU - Qiao , Haili
AU - Cheng , Aijie
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 255
EP - 275
PY - 2021
DA - 2021/02
SN - 11
DO - http://doi.org/10.4208/eajam.190520.111020 
UR - https://global-sci.org/intro/article_detail/eajam/18634.html
KW - Fractional differential equation, weak singularity, finite difference, convergence analysis, non-uniform meshes.
AB - <p style="text-align: justify;">The solutions of fractional equations with Caputo derivative often have a singularity at the initial time. Therefore, for numerical methods on uniform meshes it is difficult to achieve optimal convergence rates. To improve the convergence, Liu et al. [10]
considered a finite difference method on non-uniform meshes. Following the ideas
of [10], we introduce two more sets of non-uniform meshes and show that the corresponding discrete models have higher convergence rates. Besides, we apply the trapezoidal rule in the case of linear fractional partial differential equations. The results of
numerical experiments are consistent with the theoretical analysis.</p>