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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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A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
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by Dongwoo Sheen, Ian H. Sloan and Vidar Thomée PDF
Math. Comp. 69 (2000), 177-195 Request permission


We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval $[0,1]$, and finally applying a standard quadrature formula to this integral. The method requires the solution of a finite set of elliptic problems with complex coefficients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by finite elements.
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Additional Information
  • Dongwoo Sheen
  • Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
  • Email:
  • Ian H. Sloan
  • Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia
  • MR Author ID: 163675
  • ORCID: 0000-0003-3769-0538
  • Email:
  • Vidar Thomée
  • Affiliation: Department of Mathematics, Chalmers University of Technology, S-412 96 Göte- borg, Sweden
  • MR Author ID: 172250
  • Email:
  • Received by editor(s): March 26, 1998
  • Published electronically: April 7, 1999
  • Additional Notes: This work was partially supported by the Australian Research Council and the Korea Science & Engineering Foundation through the Global Analysis Research Center at Seoul National University.
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 69 (2000), 177-195
  • MSC (1991): Primary {65M12, 65M15, 65M99}
  • DOI:
  • MathSciNet review: 1648403