Chebyshev-Legendre谱方法解广义RLW方程的误差分析  

Error Analysis of the Chebyshev-Legendre Spectral Method for Generalised RLW Equations

作　　者：唐致娣[1] 赵廷刚[1,2] 

机构地区：[1]兰州交通大学数理与软件工程学院,兰州730070 [2]兰州城市学院,兰州730070

出　　处：《西南大学学报（自然科学版）》2014年第1期72-77,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161026)

摘　　要：考虑一类具有Dirichlet边界条件的广义RLW方程(即长波方程),通过将Legendre谱方法在Chebyshev点上实现,建立求解该方程的Chebyshev-Legendre谱方法的离散格式,这种配点法结合了Legendre方法的稳定性和Chebyshev方法计算方便的优点.选取基函数构造系数矩阵,采用矩阵分解简化方程,提高了计算效率,证明了此离散格式的稳定性和收敛性,给出了近似解的敛速估计,并进行了数值实验.In this paper, a generalized RLW equation, or long wave equation, with Dirichlet boundary con dition is discussed. The discrete scheme for numerically solving the generalized RLW equation was set up with the Chebyshev-Legendre spectral method. This method has the advantages of the stability of the Leg endre method and the simplicity of computation of the Chebyshev method. A numerical experiment verifies the good stability and convergence rate of the method, and the optimal error estimate is obtained in sense of norm.

关 键 词：广义RI w方程 Chebyshev—Legendre谱方法 稳定性 收敛性 

分 类 号：O241[理学—计算数学]