East Asian J. Appl. Math., 8 (2018), pp. 746-763.
Published online: 2018-10
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.220418.210718}, url = {http://global-sci.org/intro/article_detail/eajam/12817.html} }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.