An analysis of the L1 scheme for the subdiffusion scheme with nonsmooth data
- Submitting institution
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University College London
- Unit of assessment
- 11 - Computer Science and Informatics
- Output identifier
- 16201
- Type
- D - Journal article
- DOI
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10.1093/imanum/dru063
- Title of journal
- IMA Journal of Numerical Analysis
- Article number
- -
- First page
- 197
- Volume
- 36
- Issue
- 1
- ISSN
- 0272-4979
- Open access status
- Out of scope for open access requirements
- Month of publication
- January
- Year of publication
- 2015
- URL
-
-
- Supplementary information
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-
- Request cross-referral to
- -
- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
- -
- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
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2
- Research group(s)
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-
- Citation count
- 124
- Proposed double-weighted
- No
- Reserve for an output with double weighting
- No
- Additional information
- Differential equations involve integral operators with weakly singular kernels are a flexible class of modelling tools for describing anomalous diffusion processes. Their solutions often exhibit singular behaviour and thus are challenging to approximate. This work developed a first rigorous analysis of the most popular numerical method, i.e., the L1 scheme, and rigorously proved that the method is generally only first-order accurate, which was widely believed to be higher order. It laid the foundation for developing high-order schemes, and has inspired many follow-up works on developing high-order schemes, e.g., Jin-Lazarov-Zhou 2016 SISC, Stynes-O’Riogan-Gracia 2017 SINUM, Baffet-Hesthaven 2017 JSC.
- Author contribution statement
- -
- Non-English
- No
- English abstract
- -