A Compact Difference Scheme for the Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel
Year: 2020
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0064
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 5 : pp. 1261–1279
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Weakly singular kernel compact difference scheme time-fractional partial integro-differential equation stability convergence.
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