TY - JOUR
T1 - Efficient and Accurate Numerical Methods for Long-Wave Short-Wave Interaction Equations in the Semiclassical Limit Regime
AU - Wang , Tingchun
AU - Zhao , Xiaofei
AU - Peng , Mao
AU - Wang , Peng
JO - Journal of Computational Mathematics
VL - 5
SP - 645
EP - 665
PY - 2019
DA - 2019/03
SN - 37
DO - http://doi.org/10.4208/jcm.1807-m2015-0271
UR - https://global-sci.org/intro/article_detail/jcm/13039.html
KW - Long-wave short-wave interaction equations, Semiclassical limit, Time-splitting method, Spectral method, Compact finite difference method, Conservative properties.
AB - <p style="text-align: justify;">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 $L^1$.
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.</p>