• DOI:10.1007/s10543-022-00925-z
• Corpus ID: 234338340

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}
}

• M. Calvo, Katharina Schratz
• Published 8 May 2021
• Mathematics
• ArXiv

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) or in the dispersive parameter ε. The latter will be interesting in regimes of a small dispersive parameter. We will in particular show that in the classical BBM case P (∂x) = ∂x our Lie splitting does not require any spatial regularity, i.e, first order time convergence holds in