# Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter

@article{Calvo2022UniformlyAS, title={Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony equation with dispersive parameter}, author={Mar'ia Cabrera Calvo and Katharina Schratz}, journal={ArXiv}, year={2022}, volume={abs/2105.03732} }

Abstract. We propose a new class of uniformly accurate splitting methods for the Benjamin– Bona-Mahony equation which converge uniformly in the dispersive parameter ε. The proposed splitting schemes are furthermore asymptotic convergent and preserve the KdV limit. We carry out a rigorous convergence analysis of the splitting schemes exploiting the smoothing properties in the system. This will allow us to establish improved error bounds with gain either in regularity (for non smooth solutions…

## One Citation

Time integrators for dispersive equations in the long wave regime

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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…

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