一类二次KdV类型水波方程的多辛Fourier拟谱方法  

MULTI-SYMPLECTIC FOURIER PSEUDOSPECTRAL METHOD FOR A SECOND ORDER WAVE EQUATION OF KDV TYPE

作　　者：王俊杰[1] 王连堂[2] 

机构地区：[1]普洱学院数学与统计学院,云南普洱665000 [2]西北大学数学系,西安710127

出　　处：《数值计算与计算机应用》2014年第4期241-254,共14页Journal on Numerical Methods and Computer Applications

基　　金：云南省教育厅科学研究基金项目2013Y106

摘　　要：二次KdV类型水波方程作为一类重要的非线性方程有着许多广泛的应用前景.本文基于Hamilton系统的多辛理论研究了一类二次KdV类型水波方程的数值解法,利用Fourier拟谱方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.A second order wave equation of KdV type, a important nonlinear wave equauon, ~la~ broad application prospect. The equation was studied based on the multi-symplectic theory in Hamilton space. The multi-symplectic Fourier pseudospectral method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the second order wave equation of KdV type. The multi-symplectic scheme of the second order wave equation of KdV type with several conservation laws are presented. The numerical results for the second order wave equation of KdV type are reported, showing that the multi-symplectic Fourier pseudospectral method is an efficient algorithm with excellent long-time numerical behaviors.

关 键 词：HAMILTON系统 FOURIER拟谱方法 多辛算法 二次KdV类型水波方程 

分 类 号：O241.82[理学—计算数学]