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An exponential integrator sine pseudospectral method for the generalized improved Boussinesq equation

Chunmei Su Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China; Zentrum Mathematik, Technische Universität München, 85748, Garching bei München, Germany Gulcin M. Muslu Department of Mathematics, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

Numerical Analysis and Scientific Computing mathscidoc:2205.25007

BIT Numerical Mathematics, 61, 1397–1419, 2021.4
A Deuflhard-type exponential integrator sine pseudospectral (DEI-SP) method is proposed and analyzed for solving the generalized improved Boussinesq (GIBq) equation. The numerical scheme is based on a second-order exponential integrator for time integration and a sine pseudospectral discretization in space. Rigorous analysis and abundant experiments show that the method converges quadratically and spectrally in time and space, respectively. Finally the DEI-SP method is applied to investigate the complicated and interesting long-time dynamics of the GIBq equation.
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@inproceedings{chunmei2021an,
  title={An exponential integrator sine pseudospectral method for the generalized improved Boussinesq equation},
  author={Chunmei Su, and Gulcin M. Muslu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519154006027263278},
  booktitle={BIT Numerical Mathematics},
  volume={61},
  pages={1397–1419},
  year={2021},
}
Chunmei Su, and Gulcin M. Muslu. An exponential integrator sine pseudospectral method for the generalized improved Boussinesq equation. 2021. Vol. 61. In BIT Numerical Mathematics. pp.1397–1419. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519154006027263278.
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