Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1163–1184 | Cite as

Two numerical methods for the Zakharov-Rubenchik equations

  • Xuanxuan Zhou
  • Tingchun Wang
  • Luming ZhangEmail author


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(Nr + 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.


Zakharov-Rubenchik equations Fourier pseudospectral method Exponential wave integrator Unconditional convergence FFT 

Mathematics Subject Classification (2010)

65M12 65M70 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of ScienceNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Mathematics and StatisticsNanjing University of Information Science and TechnologyNanjingChina

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