数学物理学报 ›› 2016, Vol. 36 ›› Issue (6): 1092-1102.

• 论文 • 上一篇    下一篇

一类DGH方程的多辛Fourier拟谱方法

王俊杰1, 王连堂2   

  1. 1. 普洱学院数学系 云南普洱 665000;
    2. 西北大学数学系 西安 710127
  • 收稿日期:2016-03-18 修回日期:2016-08-12 出版日期:2016-12-26 发布日期:2016-12-26
  • 作者简介:王俊杰,ynpewjj@126.com
  • 基金资助:

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

Multi-Symplectic Fourier Pseudospectral Method for a DGH Equation

Wang Junjie1, Wang Liantang2   

  1. 1. Mathematics Department of Pu Er University, Yunnan Pu'er 665000;
    2. Mathematics Department of Northwest University, Xi'an 710127
  • Received:2016-03-18 Revised:2016-08-12 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the Natural Science Foundation of Education Department of Yunnan Province (2013Y106,2015y490) and the Pu Er University Innovation Team (CXTD003)

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.

关键词: Hamilton系统, Fourier拟谱方法, 多辛理论, DGH方程

Abstract:

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-symplectic Fourier pseudospectral 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.

Key words: Hamilton system, Fourier pseudospectral method, Multi-symplectic theory, DGH equation

中图分类号: 

  • O29