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Mathematics of Computation

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A parallel method
for time-discretization of parabolic problems
based on contour integral representation
and quadrature

Authors: Dongwoo Sheen, Ian H. Sloan and Vidar Thomée
Journal: Math. Comp. 69 (2000), 177-195
MSC (1991): Primary {65M12, 65M15, 65M99}
Published electronically: April 7, 1999
MathSciNet review: 1648403
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Abstract | References | Similar Articles | Additional Information

Abstract: 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

Ian H. Sloan
Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia

Vidar Thomée
Affiliation: Department of Mathematics, Chalmers University of Technology, S-412 96 Göte- borg, Sweden

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.
Article copyright: © Copyright 1999 American Mathematical Society