## Computing the Near and Far Future Simultaneously

Martin J. Gander

University of Geneva

Time dependent problems are often solved using time marching schemes.
Such schemes are inherently sequential in nature, and at first sight
it does not seem to be possible to work on more than one time step
simultaneously. I first present several classical attempts to obtain
time parallelism, including unsuccessful ones, and then show a new
approach introduced in 2001 by Lions, Maday and Turinici called the
parareal algorithm. I will interpreted this new algorithm in the
framework of classical time parallel algorithms, present a convergence
analysis, and illustrate the results with numerical experiments, which
indicate that indeed for certain problems, time parallel computations
are a viable strategy.