A uniformly first-order accurate method for Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime

Chunmei Su Yau Mathematical Sciences Center, Tsinghua University, 100084 Beijing, China; Zentrum Mathematik, Technische Universität München, 85748 Garching bei München, Germany Xiaofei Zhao School of Mathematics and Statistics, Computational Sciences Hubei Key Laboratory, Wuhan University, 430072 Wuhan, China

Numerical Analysis and Scientific Computing mathscidoc:2205.25006

Journal of Computational Physics, 428, (1), 110064, 2021.3
We present a uniformly first order accurate numerical method for solving the Klein-Gordon-Zakharov (KGZ) system with two dimensionless parameters 0 < ε ≤ 1 and 0 <γ ≤ 1, which are inversely proportional to the plasma frequency and the acoustic speed, respectively. In the simultaneous high-plasma-frequency and subsonic limit regime, i.e. ε < γ → 0+, the KGZ system collapses to a cubic Schrödinger equation, and the solution propagates waves with O ( ε2)-wavelength in time and meanwhile contains rapid outgoing initial layers with speed O (1/ γ ) in space due to the incompatibility of the initial data. By presenting a multiscale decomposition of the KGZ system, we propose a multiscale time integrator Fourier pseudospectral method which is explicit, efficient and uniformly accurate for solving the KGZ system for all 0 < ε < γ ≤ 1. Numerical results are reported to show the efficiency and accuracy of scheme. Finally, the method is applied to investigate the convergence rates of the KGZ system to its limiting models when ε < γ → 0+.
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@inproceedings{chunmei2021a,
  title={A uniformly first-order accurate method for Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime},
  author={Chunmei Su, and Xiaofei Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519153705542244277},
  booktitle={Journal of Computational Physics},
  volume={428},
  number={1},
  pages={110064},
  year={2021},
}
Chunmei Su, and Xiaofei Zhao. A uniformly first-order accurate method for Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime. 2021. Vol. 428. In Journal of Computational Physics. pp.110064. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519153705542244277.
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