Time integrators for dispersive equations in the long wave regime

Cabrera Calvo, María; Rousset, Frédéric; Schratz, Katharina

doi:10.1090/mcom/3745

Time integrators for dispersive equations in the long wave regime
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by María Cabrera Calvo, Frédéric Rousset and Katharina Schratz;

Math. Comp. 91 (2022), 2197-2214

DOI: https://doi.org/10.1090/mcom/3745

Published electronically: June 7, 2022

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Abstract:

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 the global error of our new schemes is of order $\tau \varepsilon$ (for the first-order scheme) and $\tau ^2 \varepsilon$ (for the second-order scheme) on time intervals of length $\mathcal {O}\left ( \frac {1}{\varepsilon }\right )$.

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