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

Shulin Wu, Baochang Shi & Chengming Huang

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

Published online: 2009-06

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  • 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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@Article{CiCP-6-883, author = {Shulin Wu, Baochang Shi and Chengming Huang}, title = {Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {4}, pages = {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).

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7710.html} }
TY - JOUR T1 - Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs AU - Shulin Wu, Baochang Shi & Chengming Huang JO - Communications in Computational Physics VL - 4 SP - 883 EP - 902 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7710.html KW - AB -

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).

Shulin Wu, Baochang Shi and Chengming Huang. (2009). Parareal-Richardson Algorithm for Solving Nonlinear ODEs and PDEs. Communications in Computational Physics. 6 (4). 883-902. doi:
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