EFFICIENT AND ACCURATE NUMERICAL METHODS FOR LONG-WAVE SHORT-WAVE INTERACTION EQUATIONS IN THE SEMICLASSICAL LIMIT REGIME

作     者：Tingchun Wang Xiaofei Zhao Mao Peng Peng Wang 

作者机构：School of Mathematics and StatisticsNanjing University of Information Science and TechnologyNanjing 210044China Department of mathematicsNational University of SingaporeSingapore 119076 Institute of MathematicsJilin UniversityChangchun 130012China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2019年第37卷第5期

页      面：645-665页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：the the National Natural Science Foundation (Grant No. 11571181) the Natural Science Foundation of Jiangsu Province (Grant No. BK20171454) Qing Lan project, thank the reviewers for their many valuable suggestions. This work was partially done while the first author was visiting Beijing Computational Science Research Center from October 3, 2013 to March 3, 2014. 

主　　题：Long-wave short-wave interaction equations Semiclassical limit Time-splitting method Spectral method Compact finite difference method Conservative properties 

摘      要：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 ap-plication 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.