一类DGH方程的多辛Fourier拟谱方法  

Multi-Symplectic Fourier Pseudospectral Method for a DGH Equation

作　　者：王俊杰[1] 王连堂[2] 

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

出　　处：《数学物理学报（A辑）》2016年第6期1092-1102,共11页Acta Mathematica Scientia

基　　金：云南省教育厅科学研究基金(2013Y106;2015y490);普洱学院创新团队项目(CXTD003)资助~~

摘　　要：DGH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.通过正则变化,构造了DGH方程的多辛哈密尔顿系统.利用Fourier拟谱方法对此哈密尔顿系统进行数值离散,并构造了一种半隐式的多辛格式.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.The DGH equation, an important nonlinear wave equation, has broad application prospect. With the canonical momenta, the multi-symplectic formulations for the DGH equation are presented. The multi-sympleetic Fourier pseudospeetral method is reviewed, and a semi-implicit scheme with certain discrete conservation laws is constructed to solve the DGH equation. The numerical experiments for DGH equation are given, 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 多辛理论 DGH方程 

分 类 号：O29[理学—应用数学]