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A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions

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Abstract

In this paper, we propose a linearly implicit Fourier pseudo-spectral scheme, which preserves the total mass and energy conservation laws for the damped nonlinear Schrödinger equation in three dimensions. With the aid of the semi-norm equivalence between the Fourier pseudo-spectral method and the finite difference method, an optimal L2-error estimate for the proposed method without any restriction on the grid ratio is established by analyzing the real and imaginary parts of the error function. Numerical results are addressed to confirm our theoretical analysis.

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Acknowledgments

The authors would like to express their sincere gratitude to the referees for their insightful comments and suggestions.

Funding

This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 11771213, 11901513), the National Key Research and Development Project of China (Grant Nos. 2018YFC0603500, 2018YFC1504205), the Yunnan Provincial Department of Education Science Research Fund Project (Grant No. 2019J0956), and the Science and Technology Innovation Team on Applied Mathematics in Universities of Yunnan.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, China

    Chaolong Jiang

  2. Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Yongzhong Song & Yushun Wang

Authors
  1. Chaolong Jiang
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  2. Yongzhong Song
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  3. Yushun Wang
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Correspondence to Yushun Wang.

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Communicated by: Jan Hesthaven

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Jiang, C., Song, Y. & Wang, Y. A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions. Adv Comput Math 46, 23 (2020). https://doi.org/10.1007/s10444-020-09781-3

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  • DOI: https://doi.org/10.1007/s10444-020-09781-3

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