Sine-Gordon方程的多辛Leap-frog格式

张宇; 邓子辰; 胡伟鹏

doi:10.3879/j.issn.1000-0887.2013.05.001

Sine-Gordon方程的多辛Leap-frog格式

doi: 10.3879/j.issn.1000-0887.2013.05.001

¹西北工业大学力学与土木建筑学院, 西安 710072;²大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116023

基金项目: 国家自然科学基金资助项目(11172239;11002115);111引智计划基金资助项目(B07050);高校博士点基金资助项目(20126102110023);大连理工大学工业装备结构分析国家重点实验室开放基金资助项目(GZ0802)

详细信息

作者简介:
张宇(1988—),男,硕士生(E-mail:yzhang@mail.nwpu.edu.cn);邓子辰(1964—),男,教授,博士生导师(通讯作者. E-mail: dweifan@nwpu.edu.cn).

中图分类号: O175.24
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出版历程
- 收稿日期: 2013-04-15
- 修回日期: 2013-05-03
- 刊出日期: 2013-05-15

Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation

¹School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnincal University, Xi’an 710072, P.R.China;²State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

摘要

摘要: 非线性发展方程由于具有多种形式的解析解而吸引着众多的研究者，借助多辛保结构理论研究了Sine-Gordon方程的多辛算法．利用Hamilton变分原理，构造出了sine-Gordon方程的多辛格式；采用显辛离散方法得到了Leap-frog多辛离散格式，该格式满足多辛守恒律；数值结果表明leap-frog多辛离散格式能够精确地模拟sine-Gordon方程的孤子解和周期解，模拟结果证实了该离散格式具有良好的数值稳定性．
- 保结构 /
- 多辛方法 /
- sine-Gordon方程 /
- leap-frog格式
Abstract: The nonlinear wave equation, which possesses various forms of analytical solutions, has been investigated widely in last several decades. The multi-symplectic method for the sine-Gordon equation in Hamilton space was proposed. Based on Hamiltonian variational principle, the multi-symplectic formulations of the sine-Gordon equation were deduced, and then, the leap-frog multi-symplectic discretization scheme was constructed using explicit symplectic discrete method. The numerical results for the sine-Gordon equation illustrate that the leap-frog multi-symplectic scheme can simulate the propagation of the soliton and the periodic solution for the sineGordon equation accurately, which show the superiority of the multi-symplectic algorithm when dealing with nonlinear evolution equations.
- structure-preserving /
- multi-symplectic method /
- sine-Gordon equation /
- leap-frog scheme

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参考文献(12)

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