Time integrators for dispersive equations in the long wave regime

2021/05/08 by María Cabrera Calvo, Calvo, María Cabrera, Frédéric Rousset +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · doi:10.48550/arxiv.2105.03731

openalex publication_date 2021/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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).

Cited by

• The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems

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