Volume 6, Issue 4
Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

Shulin Wu ,  Baochang Shi and Chengming Huang

Commun. Comput. Phys., 6 (2009), pp. 883-902.

Preview Full PDF BiBTex 93 385
  • Abstract

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 S´er. I Math., 332 (2001), pp. 661-668], is an effective algorithm to solve the timedependent problems parallel in time. This algorithm has received much interest from many researchers in the past years. We present in this paper a new variant of the parareal algorithm, which is derived by combining the original parareal algorithm and the Richardson extrapolation, for the numerical solution of the nonlinear ODEs and PDEs. Several nonlinear problems are tested to show the advantage of the new algorithm. The accuracy of the obtained numerical solution is compared with that of its original version (i.e., the parareal algorithm based on the same numerical method).

  • History

Published online: 2009-06

  • Keywords

  • AMS Subject Headings

  • Cited by