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An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
Ford, Neville J. Yan, Yubin
Ford, Neville J.
Yan, Yubin
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2017-10-31
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accepted manuscript
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Abstract
In this paper, we shall review an approach by which we can seek higher order time discretisation schemes for solving time fractional partial differential equations with nonsmooth data. The low regularity of the solutions of time fractional partial differential equations implies standard time discretisation schemes only yield first order accuracy. To obtain higher order time discretisation schemes when the solutions of time fractional partial differential equations have low regularities, one may correct the starting steps of the standard time discretisation schemes to capture the singularities of the solutions. We will consider these corrections of some higher order time discretisation schemes obtained by using Lubich's fractional multistep methods, L1 scheme and its modification, discontinuous Galerkin methods, etc. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
Citation
Ford, N. J. & Yan, Y. (2017). An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data. Fractional Calculus and Applied Analysis, 20(5), 1076-1105. https://doi.org/10.1515/fca-2017-0058
Publisher
De Gruyter
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Fractional Calculus and Applied Analysis
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Article
Language
en
Description
Invited review article for Anniversary Edition of Journal.
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ISSN
1314-2224