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Stability of the parareal algorithm. (English) Zbl 1066.65079
Kornhuber, Ralf (ed.) et al., Domain decomposition methods in science and engineering. Selected papers of the 15th international conference on domain decomposition, Berlin, Germany, July 21–25, 2003. Berlin: Springer (ISBN 3-540-22523-4/pbk). Lecture Notes in Computational Science and Engineering 40, 449-456 (2005).
Summary: We discuss the stability of the parareal algorithm for an autonomous set of differential equations. The stability function for the algorithm is derived, and stability conditions for the case of real eigenvalues are given. The general case of complex eigenvalues has been investigated by computing the stability regions numerically.
For the entire collection see [Zbl 1049.65003].

MSC:
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A30 Linear ordinary differential equations and systems
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