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Correction of High-Order Lk Approximation for Subdiffusion
Shi, Jiankang Chen, Minghua Yan, Yubin Coa, Jianxiong
Shi, Jiankang
Chen, Minghua
Yan, Yubin
Coa, Jianxiong
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2022-09-07
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Abstract
The subdiffusion equations with a Caputo fractional derivative of order $\alpha \in (0, 1)$ arise in a wide variety of practical problems, which describe the transport processes, in the force-free limit, slower than Brownian diffusion. In this work, we derive the correction schemes of the Lagrange interpolation with degree $k ( \leq 6)$ convolution quadrature, called $L_{k}$ approximation, for the subdiffusion. The key step of designing correction algorithm is to calculate the explicit form of the coefficients of $L_{k}$ approximation by the polylogarithm function or Bose-Einstein integral. To construct a $\tau_{8}$ approximation of Bose-Einstein integral, the desired $(k+1-\alpha)$th-order convergence rate can be proved for the correction $L_{k}$ scheme with nonsmooth data, which is higher than kth-order BDFk method in [Jin, Li, and Zhou, SIAM J. Sci. Comput., 39 (2017), A3129–A3152; Shi and Chen, J. Sci. Comput., (2020) 85:28]. The numerical experiments with spectral method are given to illustrate theoretical results.
Citation
Shi, J., Chen, M., Yan, Y., & Coa, J. (2022). Correction of high-order Lk Approximation for Subdiffusion. Journal of Scientific Computing, 93, 31. https://doi.org/10.1007/s10915-022-01984-8
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Springer
Journal
Journal of Scientific Computing
Research Unit
DOI
10.1007/s10915-022-01984-8
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Article
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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10915-022-01984-8
Series/Report no.
ISSN
0885-7474
EISSN
1573-7691