On the Superlinear and Linear Convergence of the Parareal Algorithm

  • Martin J. Gander
  • Stefan Vandewalle
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 55)


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.


Toeplitz Operator Euler Method Absolute Stability Bound Time Interval Superlinear Convergence 
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Copyright information

© Springer 2007

Authors and Affiliations

  • Martin J. Gander
    • 1
  • Stefan Vandewalle
    • 2
  1. 1.Section de MathématiquesUniversity of GenevaGeneva 4Switzerland
  2. 2.Department of Computer ScienceKatholieke Universiteit LeuvenLeuvenBelgium

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