Abstract
We present a novel class of integrators for differential equations that are suitable for parallel in time computation, whose structure can be considered as a generalization of the extrapolation methods. Starting with a low order integrator (preferably a symmetric second order one) we can build a set of second order schemes by few compositions of this basic scheme that can be computed in parallel. Then, a proper linear combination of the results (obtained from the order conditions associated to the corresponding Lie algebra) allows us to obtain new higher order methods. In this letter we present the structure of the methods, how to obtain several methods, we notice some order barriers that depend on the structure of the compositions used and finally, we show how this analysis can be further carried to obtain new and higher order schemes.
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