半直线上Kortewego-de Vries方程的Laguerre谱配置方法  

Generalized Laguerre Spectral-Collocation Method for KdV Equations on the Half Line

作　　者：王其霞 苗伊浩 王天军[1] 

机构地区：[1]河南科技大学 数学与统计学院,河南 洛阳

出　　处：《应用数学进展》2020年第9期1583-1588,共6页Advances in Applied Mathematics

摘　　要：以Laguerre-Gauss-Radau节点为配置点,用带松弛因子的Lagrange插值函数逼近半直线上的Kortewego-de Vries方程初边值问题的理论解,给出算法格式和相应的数值结果,表明所提算法格式的有效性和高精度。对理论解中参数的不同取值,通过适当地选择插值函数中的松弛因子,数值解可以很好地匹配理论解,而且所给算法对长时间的计算仍然有效。Interpolation function approximations with relaxation factor by using Laguerre-Gauss-Radau nodes as collocation points to the Korteweg-de Vries equation on semi-infinite intervals are considered. The validity and high accuracy of the proposed algorithm are demonstrated. By choosing the relaxation factor of the interpolation function properly, the numerical solution can match the theoretical solution well, and the algorithm is still valid for a long time.

关 键 词：Kortewego-de Vries方程初边值问题 Laguerre函数谱配置方法 Laguerre-Gauss-Radau节点 半直线 

分 类 号：O17[理学—数学]