Here is a short introduction to waveform relaxation. When talking about the time-parallel method like parareal or PITA or other methods, one should distinguish between the dissipative and the conservative (Hamiltonian) ODE systems. The latter seems more difficult to parallelize in time dimension by partitioning to time sub-intervals. Here is an analysis of parareal for Hamiltonian systems. The dissipative system is easier because the error caused at initial time $u_0$ tends to disappear due to the dissipation $u(t)=\exp(-\lambda t)u_0,$ $\lambda>0.$

Here is a short introduction to waveform relaxation. When talking about the time-parallel method like parareal or PITA or other methods, one should distinguish between the dissipative and the conservative (Hamiltonian) ODE systems. The latter seems more difficult to parallelize in time dimension by partitioning to time sub-intervals. Here is an analysis of parareal for Hamiltonian systems. The dissipative system is easier because the error caused at initial time $u_0$ tends to disappear due to the dissipation $u(t)=\exp(-\lambda t)u_0,$ $\mathrm{Re}\,\lambda>0.$