Abstract
A time integration method for the resolution of ordinary and partial dierential equations is proposed. The method consists in computing a formal solution as a (eventually divergent) time series. Next, the Borel resummation method is applied to deduce an (sectorial) analytical solution. The speed and spectral properties of the scheme are analyzed through some examples. Applications to fluid mechanics are presented. ResumOn propose une methode numerique d'integration temporelle d'´ equations di´ erentielles ou aux derivees partielles. Cette methode consiste d'abordcalculer une solution sous forme de serie formelle, dont le rayon de convergence peutnul. Ensuite, la methode de resommation de Borel- Laplace est utilisee pour deduire une solution analytique (dans un secteur) de l'´ equation. La rapidite et les proprietes geometriques du schema sont analyseestravers quelques exemples. Des applications en mecanique des fluides sont presentees.
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