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An analysis of the modified L1 scheme for time-fractional partial differential equations with nonsmooth data
Yan, Yubin Khan, Monzorul Ford, Neville J.
Yan, Yubin
Khan, Monzorul
Ford, Neville J.
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2018-01-11
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Abstract
We introduce a modified L1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous cases. Jin \et (2016, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data, IMA J. of Numer. Anal., 36, 197-221) established an $O(k)$ convergence rate for the L1 scheme for smooth and nonsmooth initial data for the homogeneous problem, where $k$ denotes the time step size. We show that the modified L1 scheme has convergence rate $O(k^{2-\alpha}), 0< \alpha <1$ for smooth and nonsmooth initial data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
Citation
Yan, Y. , Khan, M., & Ford, N. J. (2018). An analysis of the modified L1 scheme for time-fractional partial differential equations with nonsmooth data. SIAM Journal on Numerical Analysis (SINUM), 56(1), 210-227. https://doi.org/10.1137/16M1094257
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Society for Industrial and Applied Mathematics
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SIAM Journal on Numerical Analysis (SINUM)
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DOI
10.1137/16M1094257
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Article
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en
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First Published in SIAM Journal on Numerical Analysis (SINUM), 56(1), 2018, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
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ISSN
0036-1429
EISSN
1095-7170