Time integrators for dispersive equations in the long wave regime

05/08/2021

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by   María Cabrera Calvo, et al.

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We introduce a novel class of time integrators for dispersive equations which allow us to reproduce the dynamics of the solution from the classical ε = 1 up to long wave limit regime ε≪ 1 on the natural time scale of the PDE t= 𝒪(1/ε). Most notably our new schemes converge with rates at order τε over long times t= 1/ε.