TY - JOUR
T1 - A High Order Scheme for Fractional Differential Equations with the Caputo-Hadamard Derivative
AU - Ye , Xingyang
AU - Cao , Junying
AU - Xu , Chuanju
JO - Journal of Computational Mathematics
VL - 3
SP - 615
EP - 640
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2312-m2023-0098
UR - https://global-sci.org/intro/article_detail/jcm/23552.html
KW - Caputo-Hadamard derivative, Fractional differential equations, High order
scheme, Stability and convergence analysis.
AB - <p style="text-align: justify;">In this paper, we consider numerical solutions of the fractional diffusion equation with
the $α$ order time fractional derivative defined in the Caputo-Hadamard sense. A high
order time-stepping scheme is constructed, analyzed, and numerically validated. The contribution of the paper is twofold: 1) regularity of the solution to the underlying equation
is investigated, 2) a rigorous stability and convergence analysis for the proposed scheme
is performed, which shows that the proposed scheme is $3 + α$ order accurate. Several
numerical examples are provided to verify the theoretical statement.</p>