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 -

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.