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Galerkin methods for the Davey–Stewartson equations

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  • Gao, Yali
  • Mei, Liquan
  • Li, Rui

Abstract

In this paper, we propose two Galerkin methods to investigate the evolution of the Davey–Stewartson equations. The extrapolated Crank–Nicolson scheme and decoupled semi-implicit multistep scheme are employed to increase the order of the time discrete accuracy, which only requires the solutions of a linear system at each time step. Four numerical experiments are presented to illustrate the features of the proposed numerical methods, such as the optimal convergence order, the conservation variable and the application in rogue waves.

Suggested Citation

  • Gao, Yali & Mei, Liquan & Li, Rui, 2018. "Galerkin methods for the Davey–Stewartson equations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 144-161.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:144-161
    DOI: 10.1016/j.amc.2018.01.044
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
    2. Babaoglu, Ceni, 2008. "Long-wave short-wave resonance case for a generalized Davey–Stewartson system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 48-54.
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