Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs

Year:    2009

Communications in Computational Physics, Vol. 6 (2009), Iss. 4 : pp. 883–902

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 Sér. I Math., 332 (2001), pp. 661-668], is an effective algorithm to solve the time-dependent 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).

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-CiCP-7710

Communications in Computational Physics, Vol. 6 (2009), Iss. 4 : pp. 883–902

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords: