Two high-order time discretization schemes for subdiffusion problems with nonsmooth data
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AbstractAbstract Two new high-order time discretization schemes for solving subdiffusion problems with nonsmooth data are developed based on the corrections of the existing time discretization schemes in literature. Without the corrections, the schemes have only a first order of accuracy for both smooth and nonsmooth data. After correcting some starting steps and some weights of the schemes, the optimal convergence orders O(k 3–α ) and O(k 4–α ) with 0 < α < 1 can be restored for any fixed time t for both smooth and nonsmooth data, respectively. The error estimates for these two new high-order schemes are proved by using Laplace transform method for both homogeneous and inhomogeneous problem. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
CitationFractional Calculus and Applied Analysis, volume 23, issue 5, page 1349-1380
PublisherWalter de Gruyter GmbH
DescriptionFrom Crossref journal articles via Jisc Publications Router
History: issued 2020-10-01, ppub 2020-10-27, epub 2020-11-13