Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data
Affiliation
University of Chester, Lvliang University, Jimei University, Indian Institute of Technology BombayPublication Date
2020-05-19
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Two higher order time stepping methods for solving subdiffusion problems are studied in this paper. The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwald-Letnikov formulae introduced in Tian et al. [Math. Comp. 84 (2015), pp. 2703-2727]. After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders $O(k^2)$ and $ O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of our time stepping schemes to various other fractional evolution equations. Finally, some numerical examples are given to show that the numerical results are consistent with the proven theoretical results.Citation
Wang, Y., Yan, Y., Yan, Y. et al. (2020). Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data. Journal of Scientific Computing, 83, 40.Publisher
Springer LinkJournal
Journal of Scientific ComputingType
ArticleEISSN
1573-7691ae974a485f413a2113503eed53cd6c53
10.1007/s10915-020-01223-y
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