Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs (Communications in Computational Physics, 2009)
The parareal algorithm, proposed firstly by Lions et al. [J. L. Lions, Y. Maday,and G. Turinici, A "parareal" in time discretization of PDE's, C.R. Acad. Sci.Paris Sér. I Math., 332 (2001), pp. 661-668], is an effective algorithm to solve the time-dependentproblems parallel in time. This algorithm has received much interest frommany researchers in the past years. We present in this paper a new variant of theparareal algorithm, which is derived by combining the original parareal algorithmand the Richardson extrapolation, for the numerical solution of the nonlinear ODEsand PDEs. Several nonlinear problems are tested to show the advantage of the newalgorithm. The accuracy of the obtained numerical solution is compared with that ofits original version (i.e., the parareal algorithm based on the same numerical method).