TY - JOUR
T1 - A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel
AU - Guo , Jing
AU - Xu , Da
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1261
EP - 1279
PY - 2020
DA - 2020/07
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0064
UR - https://global-sci.org/intro/article_detail/aamm/17748.html
KW - Weakly singular kernel, compact difference scheme, time-fractional partial integro-differential equation, stability, convergence.
AB - <p style="text-align: justify;">In this paper, we construct a compact difference scheme for the time-fractional partial integro-differential equation. This model involves two nonlocal terms in time, i.e., a Caputo time-fractional derivative and an integral term with memory. We obtain the stability and the discrete $L_{2}$ convergence with second-order in time and fourth-order in space by the energy method. Two numerical examples are provided to confirm the theoretical results.</p>