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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problem
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by Natalia Kopteva HTML | PDF
Math. Comp. 90 (2021), 19-40 Request permission


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. An L2-type discrete fractional-derivative operator of order $3-\alpha$ is considered on nonuniform temporal meshes. Sufficient conditions for the inverse-monotonicity of this operator are established, which yields sharp pointwise-in-time error bounds on quasi-graded temporal meshes with arbitrary degree of grading. In particular, those results imply that milder (compared to the optimal) grading yields optimal convergence rates in positive time. Semi-discretizations in time and full discretizations are addressed. The 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:
  • Received by editor(s): May 22, 2019
  • Received by editor(s) in revised form: March 28, 2020, and April 3, 2020
  • Published electronically: July 14, 2020
  • Additional Notes: This research was supported by Science Foundation Ireland Grant SFI/12/IA/1683.
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 19-40
  • MSC (2000): Primary 65M15, 65M60
  • DOI:
  • MathSciNet review: 4166451