Abstract
The parareal algorithm, recalled in section 2 below, allows one to solve evolution equations on (possibly massively) parallel architectures. The two building blocks of the algorithms are a coarse-discretization predictor (solved sequentially) and a fine-discretization corrector (solved in parallel). First developed in [9] and slightly modified in [3], which is the algorithm presented below, the parareal algorithm has received quite a bit of attention lately; see e.g. [1, 2, 4, 5, 6, 7, 10] and their references. Section 3 recalls some results on the parareal algorithm when it is used to solve ordinary and partial differential equations. One of the main shortcomings of the parareal algorithm is that, as a predictor corrector scheme, it may generate high-frequency instabilities.
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