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A new numerical scheme for the nonlinear Schrödinger equation with wave operator

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Abstract

In this paper, a new compact finite difference scheme is proposed for a periodic initial value problem of the nonlinear Schrödinger equation with wave operator. This is an explicit scheme of four levels with a discrete conservation law. The unconditional stability and convergence in maximum norm with order \(O(h^{4}+\tau ^{2})\) are verified by the energy method. Those theoretical results are proved by a numerical experiment and it is also verified that this scheme is better than the previous scheme via comparison.

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Acknowledgments

The authors would like to express their sincere thanks and gratitude to the editors and reviewers for their insightful comments and suggestions for the improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Anhui Science and Technology University, Fengyang, 233100, China

    Xin Li & Ting Zhang

  2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Luming Zhang

Authors
  1. Xin Li
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  2. Luming Zhang
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  3. Ting Zhang
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Corresponding author

Correspondence to Xin Li.

Additional information

This work is supported by the Natural Science Foundation of Anhui Province (No. 1508085QB41) and the University Natural Science Research key Project of Anhui Province (No. KJ2015A242).

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Li, X., Zhang, L. & Zhang, T. A new numerical scheme for the nonlinear Schrödinger equation with wave operator. J. Appl. Math. Comput. 54, 109–125 (2017). https://doi.org/10.1007/s12190-016-1000-4

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  • DOI: https://doi.org/10.1007/s12190-016-1000-4

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