We introduce a novel class of time integrators for dispersive equations which allow us to reproduce the dynamics of the solution from the classical $ \varepsilon = 1$ up to long wave limit regime $ \varepsilon \ll 1 $ on the natural time scale of the PDE $t= \mathcal{O}(\frac{1}{\varepsilon})$. Most notably our new schemes converge with rates at order $\tau \varepsilon$ over long times $t= \frac{1}{\varepsilon}$.
翻译:我们为分散式方程式引入了新型的时间集成器。 这使得我们能够从古典的 $ \ varepsilon = 1美元 = 1美元 = 1美元 = 1美元 = 1美元 = 1美元 PDE $t = mathcal{O} (\ frac {1\ tunvarepsilon} ) 的自然时间规模。 最显著的是,我们的新方案与以$ tau \ \ varepsilon = 1美元 = grac = 1 unvarepsilon} 的汇率趋同。