Parallel adaptive time domain decomposition for stiff systems of ODEs/DAEs

Time domain decompositions to solve ODEs/DAEs have been numerically investigated by introducing adaptivity in the definition of the refinement of the time grid, time domain splitting. We show that the parareal method [Lions J-L, Maday Y, Turinici G. Résolution d’EDP par un schéma en temps “pararéel”, CRAS Sér I Math 2000;332(7):661–8] is a particular case of the multiple shooting method of Deuflhard. Numerical evidences of the limitation of this method to solve very stiff problems are exhibited, leading us to propose an adaptive parallel extrapolation method.