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

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Abstract

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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Acknowledgements

The authors are very grateful to the anonymous referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of the paper.

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Authors and Affiliations

  1. South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou, 510631, China

    Gengen Zhang

  2. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

    Chunmei Su

  3. Zentrum Mathematik, Technische Universität München, 85748, Garching bei München, Germany

    Chunmei Su

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  1. Gengen Zhang
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Correspondence to Chunmei Su.

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The work is supported by the National Natural Science Foundation of China (Grant No. 11701110), the China Postdoctoral Science Foundation (Grant No. 2020M682746) (G. Zhang), and the Alexander von Humboldt Foundation (C. Su).

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Zhang, G., Su, C. A Conservative Linearly-Implicit Compact Difference Scheme for the Quantum Zakharov System. J Sci Comput 87, 71 (2021). https://doi.org/10.1007/s10915-021-01482-3

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