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BDF2 ADI orthogonal spline collocation method for the fractional integro-differential equations of parabolic type in three dimensions
Yan, Yubin Qiao, Leijie Wang, Ruru Hendy, Ahmed S.
Yan, Yubin
Qiao, Leijie
Wang, Ruru
Hendy, Ahmed S.
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Publication Date
2023-12-13
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Abstract
In this paper, we are concerned with constructing a fast and an efficient alternating direction implicit (ADI) scheme for the fractional parabolic integro-differential equations (FPIDE) with a weakly singular kernel in three dimensions (3D). Our constructed scheme is based on a second-order backward differentiation formula (BDF2) for temporal discretization, orthogonal spline collocation (OSC) method for spatial discretization and a second-order fractional quadrature rule proposed by Lubich for the Riemann-Liouville fractional integral. The stability and convergence of the constructed numerical scheme are derived. Finally, some numerical examples are given to illustrate the accuracy and validity of the BDF2 ADI OSC method. Based on the obtained results, the numerical results are in line with the theoretical ones.
Citation
Wang, R., Yan, Y., Hendy, A. S., & Qiao, L. (2023). BDF2 ADI orthogonal spline collocation method for the fractional integro-differential equations of parabolic type in three dimensions. Computers & Mathematics with Applications, 155, 126-141. https://doi.org/10.1016/j.camwa.2023.12.008
Publisher
Elsevier
Journal
Computers & Mathematics with Applications
Research Unit
DOI
10.1016/j.camwa.2023.12.008
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PubMed Central ID
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Article
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ISSN
0898-1221