@Article{EAJAM-8-746,
author = {Chengming Huang and Shu-Lin Wu},
title = {Convergence of Parareal Algorithms for PDEs with Fractional Laplacian and a Non-Constant Coefficient},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {8},
number = {4},
pages = {746--763},
abstract = {<p style="text-align: justify;">The convergence of Parareal-Euler and -LIIIC2 algorithms using the backward
Euler method as a $\mathscr{G}$-propagator for the linear problem $U^′
(t)+α(t)A^ηU(t)=f(t)$ with
a non-constant coefficient $α$ is studied. We propose to employ the propagator $G$ to a
constant model $U^′(t)+βA^ ηU(t)=f(t)$ with a special coefficient β instead of applying
both propagators $\mathscr{G}$ and $\mathscr{F}$ to the same target model. We established a simple formula
to find an optimal parameter $β_{opt}$, minimising the convergence factor for all mesh ratios.
Numerical results confirm the proximity of theoretical optimal $β_{opt}$ to the optimal
numerical parameter.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.220418.210718},
url = {http://global-sci.org/intro/article_detail/eajam/12817.html}
}