@Article{CiCP-6-4,
author = {},
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 = {<p style="text-align: justify;">The parareal algorithm, proposed firstly by Lions et al. [J. L. Lions, Y. Maday,
and G. Turinici, A &quot;parareal&quot; in time discretization of PDE&#39;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).</p>},
issn = {1991-7120},
doi = {https://doi.org/2009-CiCP-7710},
url = {https://global-sci.com/article/81174/parareal-richardson-algorithm-for-solving-nonlinear-odes-and-pdes}
}