Korteweg-de Vries方程的时空谱配置方法  

SPACE-TIME SPECTRAL COLLOCATION METHOD FOR KORTEWEG-DE VRIES EQUATION

作　　者：马亚楠 王天军[1] 李冰冰 Ma Yanan;Wang Tianjun;Li Bingbing(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471003,China)

机构地区：[1]河南科技大学数学与统计学院,洛阳471003

出　　处：《数值计算与计算机应用》2021年第4期351-360,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11371123,11171227);河南省自然科学基金(202300410156)资助.

摘　　要：针对全直线上的KdV方程构造了时空全离散Legendre-Hermite谱配置格式,也就是在时间方向上用Legendre-Gauss-Lobatto节点为配置点,在空间方向上用Hermite-Gauss节点为配置点.构造得到一个非线性矩阵方程.将其化为非线性方程组,利用通常的不动点迭代求解.数值实验表明这种方法的有效性.A Legendre-Hermite spectral collocation scheme is constructed for Korteweg-de Vries(KdV)equation on the whole line by using the Legendre collocation method in time,and the Hermite spectral collocation method in space,which is a nonlinear matrix equation that is changed to a nonlinear systems and can be solved by the usual fixed point iteration.Numerical results demonstrate the efficiency of the method.

关 键 词：Korteweg-de Vries方程 时空谱配置方法 全直线. 

分 类 号：O241.7[理学—计算数学]