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A Conservative Linearly-Implicit Compact Difference Scheme for the Quantum Zakharov System

Gengen Zhang South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou, 510631, China Chunmei Su Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China; Zentrum Mathematik, Technische Universität München, 85748, Garching bei München, Germany

Numerical Analysis and Scientific Computing mathscidoc:2205.25008

Journal of Scientific Computing, 87, 71, 2021.4
This paper is devoted to developing and analysing a highly accurate conservative method for solving the quantum Zakharov system. The scheme is based on a linearly-implicit compact finite difference discretization and conserve the mass as well as energy in discrete level. Detailed numerical analysis is presented which shows the method is fourth-order accurate in space and second-order accurate in time. Several numerical examples are reported to confirm the conservation properties and high accuracy of the proposed scheme. Finally the compact scheme is applied to study the convergence rate of the quantum Zakharov system to its limiting model in the semi-classical limit.
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@inproceedings{gengen2021a,
  title={A Conservative Linearly-Implicit Compact Difference Scheme for the Quantum Zakharov System},
  author={Gengen Zhang, and Chunmei Su},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519154429169707279},
  booktitle={Journal of Scientific Computing},
  volume={87},
  pages={71},
  year={2021},
}
Gengen Zhang, and Chunmei Su. A Conservative Linearly-Implicit Compact Difference Scheme for the Quantum Zakharov System. 2021. Vol. 87. In Journal of Scientific Computing. pp.71. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519154429169707279.
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