A Lawson-type exponential integrator for the Korteweg–de Vries equation

Alexander Ostermann University of Innsbruck , 6020 Innsbruck, Austria Chunmei Su University of Innsbruck , 6020 Innsbruck, Austria

Numerical Analysis and Scientific Computing mathscidoc:2205.25014

IMA Journal of Numerical Analysis, 40, (4), 2399–2414, 2020.10
We propose an explicit numerical method for the periodic Korteweg–de Vries equation. Our method is based on a Lawson-type exponential integrator for time integration and the Rusanov scheme for Burgers’ nonlinearity. We prove first-order convergence in both space and time under a mild Courant–Friedrichs–Lewy condition τ=O(h)⁠, where τ and h represent the time step and mesh size for solutions in the Sobolev space H^3((−π,π))⁠, respectively. Numerical examples illustrating our convergence result are given.
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@inproceedings{alexander2020a,
  title={A Lawson-type exponential integrator for the Korteweg–de Vries equation },
  author={Alexander Ostermann, and Chunmei Su},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519163120326962293},
  booktitle={IMA Journal of Numerical Analysis},
  volume={40},
  number={4},
  pages={2399–2414},
  year={2020},
}
Alexander Ostermann, and Chunmei Su. A Lawson-type exponential integrator for the Korteweg–de Vries equation . 2020. Vol. 40. In IMA Journal of Numerical Analysis. pp.2399–2414. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519163120326962293.
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