# Convergence error estimates at low regularity for time discretizations of KdV

@article{Rousset2022ConvergenceEE, title={Convergence error estimates at low regularity for time discretizations of KdV}, author={Frederic Rousset and Katharina Schratz}, journal={ArXiv}, year={2022}, volume={abs/2102.11125} }

We consider various filtered time discretizations of the periodic Korteweg–de Vries equation: a filtered exponential integrator, a filtered Lie splitting scheme as well as a filtered resonance based discretisation and establish convergence error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows to prove convergence in L for rough data u0 ∈ H , s > 0 with an explicit convergence rate.

## 5 Citations

### An unfiltered low-regularity integrator for the KdV equation with solutions below H1

- MathematicsArXiv
- 2022

. This article is concerned with the construction and analysis of new time discretizations for the KdV equation on a torus for low-regularity solutions below H 1 . New harmonic analysis tools,…

### Bridging the gap: symplecticity and low regularity on the example of the KdV equation

- MathematicsArXiv
- 2022

Recent years have seen an increasing amount of research devoted to the development of so-called resonance-based methods for dispersive nonlinear partial diﬀerential equations. In many situations,…

### Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity

- MathematicsJ. Comput. Appl. Math.
- 2023

### Approximations of dispersive PDEs in the presence of low-regularity randomness

- Mathematics, Computer ScienceArXiv
- 2022

A novel combinatorial structure called paired decorated forests which are two decorated trees whose decorations on the leaves come in pair are introduced which allows for low regularity approximations to the expectation E ( | u k ( τ, v η ) | 2 ) , where u k denotes the k -th Fourier coeﬃcient of the solution u of the dispersive equation and v x the associated random initial data.

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

- MathematicsBIT Numerical Mathematics
- 2022

A rigorous convergence analysis of the splitting schemes exploiting the smoothing properties in the Benjamin– Bona-Mahony equation is carried out, showing that in the classical BBM case P (∂x) = ∂x the authors' Lie splitting does not require any spatial regularity.

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