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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
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by Natalia Kopteva HTML | PDF
Math. Comp. 88 (2019), 2135-2155 Request permission

Abstract:

An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha \in (0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple framework for the analysis of the error of L1-type discretizations on graded and uniform temporal meshes in the $L_\infty$ and $L_2$ norms. This framework is employed in the analysis of both finite difference and finite element spatial discretiztions. Our theoretical findings are illustrated by numerical experiments.
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Additional Information
  • Natalia Kopteva
  • Affiliation: Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
  • MR Author ID: 610720
  • ORCID: 0000-0001-7477-6926
  • Email: natalia.kopteva@ul.ie
  • Received by editor(s): September 23, 2017
  • Received by editor(s) in revised form: September 25, 2017, October 18, 2017, May 19, 2018, and October 16, 2018
  • Published electronically: January 23, 2019
  • Additional Notes: The author acknowledges financial support from Science Foundation Ireland Grant SFI/12/IA/1683.
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2135-2155
  • MSC (2010): Primary 65M06, 65M15, 65M60
  • DOI: https://doi.org/10.1090/mcom/3410
  • MathSciNet review: 3957889