Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data
MetadataShow full item record
AbstractAbstract: 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 Grünwald–Letnikov formulae introduced in Tian et al. (Math Comput 84:2703–2727, 2015). After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders O(k2) and O(k3), 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.
CitationJournal of Scientific Computing, volume 83, issue 3, page 40
DescriptionFrom Springer Nature via Jisc Publications Router
History: received 2019-07-19, rev-recd 2020-04-08, accepted 2020-04-18, registration 2020-04-18, pub-electronic 2020-05-19, online 2020-05-19, pub-print 2020-06
Publication status: Published
Funder: University of Chester