A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
Journal article, 2000

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 , 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.


D Sheen

I. H. Sloan

Vidar Thomee

University of Gothenburg

Department of Mathematics

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 69 229 177-195

Subject Categories

Computational Mathematics


Basic sciences



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