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Two numerical methods for the Zakharov-Rubenchik equations

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Abstract

Two numerical methods are presented for the approximation of the Zakharov-Rubenchik equations (ZRE). The first one is the finite difference integrator Fourier pseudospectral method (FFP), which is implicit and of the optimal convergent rate at the order of O(N−r + τ2) in the discrete L2 norm without any restrictions on the grid ratio. The second one is to use the Fourier pseudospectral approach for spatial discretization and exponential wave integrator for temporal integration. Fast Fourier transform is applied to the discrete nonlinear system to speed up the numerical computation. Numerical examples are given to show the efficiency and accuracy of the new methods.

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Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu, China

    Xuanxuan Zhou & Luming Zhang

  2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Tingchun Wang

Authors
  1. Xuanxuan Zhou
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  2. Tingchun Wang
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  3. Luming Zhang
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Correspondence to Luming Zhang.

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Communicated by: Jon Wilkening

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Foundation item: Supported by National Nature Science Foundation of China No.11571181.

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Zhou, X., Wang, T. & Zhang, L. Two numerical methods for the Zakharov-Rubenchik equations. Adv Comput Math 45, 1163–1184 (2019). https://doi.org/10.1007/s10444-018-9651-3

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  • DOI: https://doi.org/10.1007/s10444-018-9651-3

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