数值计算与计算机应用
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数值计算与计算机应用  2014, Vol. 35 Issue (4): 241-254    DOI:
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一类二次KdV类型水波方程的多辛Fourier拟谱方法
王俊杰1, 王连堂2
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
MULTI-SYMPLECTIC FOURIER PSEUDOSPECTRAL METHOD FOR A SECOND ORDER WAVE EQUATION OF KDV TYPE
Wang Junjie1, Wang Liantang2
1. Pu Er University, Mathematics and Statistical Institute, Pu'er 665000, Yunnan, China;
2. Northwest University, Mathematics Department, Xi'an 710127, China
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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.
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关键词Hamilton系统   Fourier拟谱方法   多辛算法   二次KdV 类型水波方程     
Abstract: A second order wave equation of KdV type, a important nonlinear wave equation, has 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.
Key wordsHamilton space   Fourier pseudospectral method   Multi-symplectic theory   A second order wave equation of KdV type   
收稿日期: 2013-10-13;
基金资助:

云南省教育厅科学研究基金项目2013Y106.

引用本文:   
. 一类二次KdV类型水波方程的多辛Fourier拟谱方法[J]. 数值计算与计算机应用, 2014, 35(4): 241-254.
. MULTI-SYMPLECTIC FOURIER PSEUDOSPECTRAL METHOD FOR A SECOND ORDER WAVE EQUATION OF KDV TYPE[J]. Journal of Numerical Methods and Computer Applicat, 2014, 35(4): 241-254.
 
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