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Published in:
2007 | OriginalPaper | Chapter
On the Superlinear and Linear Convergence of the Parareal Algorithm
Authors : Martin J. Gander, Stefan Vandewalle
Published in: Domain Decomposition Methods in Science and Engineering XVI
Publisher: Springer Berlin Heidelberg
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The parareal algorithm is a method to solve time dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on some new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals, and linear convergence for unbounded intervals.