Volume 37, Issue 5
Efficient and Accurate Numerical Methods for Long-Wave Short-Wave Interaction Equations in the Semiclassical Limit Regime

Tingchun Wang ,  Xiaofei Zhao ,  Mao Peng and Peng Wang


J. Comp. Math., 37 (2019), pp. 645-665.

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  • Abstract

This paper focuses on performance of several efficient and accurate numerical methods for the long-wave short-wave interaction equations in the semiclassical limit regime. The key features of the proposed methods are based on: (i) the utilization of the first-order or second-order time-splitting method to the nonlinear wave interaction equations; (ii) the application of Fourier pseudo-spectral method or compact finite difference approximation to the linear subproblem and the spatial derivatives; (iii) the adoption of the exact integration of the nonlinear subproblems and the ordinary differential equations in the phase space. The numerical methods under study are efficient, unconditionally stable and higher-order accurate, they are proved to preserve two invariants including the position density in L1. Numerical results are reported for case studies with different types of initial data, these results verify the conservation laws in the discrete sense, show the dependence of the numerical solution on the time-step, mesh-size and dispersion parameter ε, and demonstrate the behavior of nonlinear dispersive waves in the semi-classical limit regime.

  • History

Published online: 2019-03

  • AMS Subject Headings

65M06, 65M12

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