Volume 12, Issue 5
A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel

Jing Guo & Da Xu

Adv. Appl. Math. Mech., 12 (2020), pp. 1261-1279.

Published online: 2020-07

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  • Abstract

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.

  • Keywords

Weakly singular kernel, compact difference scheme, time-fractional partial integrodifferential equation, stability, convergence.

  • AMS Subject Headings

45K05, 65M06, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1261, author = {Jing Guo , and Da Xu , }, title = {A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {5}, pages = {1261--1279}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0064}, url = {http://global-sci.org/intro/article_detail/aamm/17748.html} }
TY - JOUR T1 - A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel AU - Jing Guo , AU - Da Xu , 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 integrodifferential 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.

Jing Guo & Da Xu. (2020). A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel. Advances in Applied Mathematics and Mechanics. 12 (5). 1261-1279. doi:10.4208/aamm.OA-2019-0064
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