[1]闫静叶,孙建强.复修正KdV方程的高阶保能量方法[J].江西师范大学学报(自然科学版),2016,40(02):209-213.
　YAN Jingye,SUN Jianqiang.The High Order Energy Preserving Method for the Complex Modified KdV Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2016,40(02):209-213.
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复修正KdV方程的高阶保能量方法()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年02期
页码:
209-213
栏目:
出版日期:
2016-03-25

文章信息/Info

Title:
The High Order Energy Preserving Method for the Complex Modified KdV Equation
作者:
闫静叶;孙建强
海南大学信息科学技术学院数学系,海南 海口 570228
Author(s):
YAN Jingye; SUN Jianqiang
College of Information Science and Technology,Hainan University,Haikou Hainan 570228,China
关键词:
平均向量场方法;  保能量方法;  复修正KdV方程;  孤立波
Keywords:
average vector field method;  energy-preserving method;  the complex modified KdV equation;  the solitary wave
分类号:
O 241.5
文献标志码:
A
摘要:
利用4阶平均向量场方法和拟谱方法构造了复修正KdV方程的高阶保能量平均向量场格式,并利用构造的高阶保能量格式数值模拟了方程孤立波的演化行为.数值结果表明:构造的4阶格式具有好的稳定性,可以很好地模拟孤立波的演化行为,并且精确保持方程的能量守恒特性.
Abstract:
The fourth order energy preserving scheme for the complex modified KdV equation is obtained by applying the fourth order average vector field method(AVF)and the Fourier pseudospectral method.The new fourth order energy preserving scheme is applied to simulate the behaviors of solitary waves of the KdV equation.Numerical results show that the fourth order scheme has a nice stability and can well simulate the solitary wave evolution behaviors of the complex modified KdV equation in long time,moreover preserve the discrete energy conservation of the system.

参考文献/References:

[1] Aydin A,Karasözen B.Multisymplectic box schemes for the complex modified Korteweg-de equation.[J].J Math Phys,2010,51(8):60-63.
[2] Ascher U M,McLachlan R I.On symplectic and mutisymplectic schemes for the KdV equation [J].J Sci Comput,2005,25(1):83-104.
[3] Wang Yushun,Wang Bing,Chen Xin.Multi-symplectic Euler-box scheme for the KdV equation [J].Chin Phys Lett,2007,24(2):312-314.
[4] 秦孟兆,王雨顺.偏微分方程的保结构算法 [M].杭州:浙江科学技术出版社,2011.
[5] Hong Jialin,Liu Ying.Multisymplecticity of the centred box scheme for a class of Hamiltonian PDEs and an application to quasi-periodically solitary waves [J].Math Comput Model,2004,39(9/10):1035-1047.
[6] Feng Kang,Qin Mengzhao.Symplectic geometric algorithms for Hamilton systems [M].Hangzhou:Zhejiang Science and Technology Publishing House,2010.
[7] 冯康,秦孟兆.哈密尔顿系统的辛几何法 [M].杭州:浙江科学技术出版社,2003.
[8] 王雨顺,王斌,秦孟兆.偏微分方程的局部保结构算法 [J].中国科学,2008,38(4):377-397.
[9] Gong Yuezheng,Cai Jiaxiang,Wang Yushun.Some new structure-preserving algorithms general muti-symplectic formulations of Hamiltonian PDEs [J].J Comput Phys,2014,279(1):80-102.
[10] 蒋朝龙,黄荣芳,孙建强.耦合非线性薛定谔方程的平均离散梯度法 [J].工程数学学报,2014,31(5):707-718.
[11] 李昊晨,孙建强,骆思宇.非线性薛定谔方程的平均向量场方法 [J].计算数学,2013,35(1):59-66.
[12] Celledoni E,Grimm V,Mclachlan R I,et al.Preserving energy resp.dissipation in numerical PDEs using the “average vector field” method [J].J Comput Phys,2012,231(20):6770-6789.
[13] Quispel G R W,McLaren D I.A new class of energy-preserving numerical integration methods [J].J Phys A:Math Theor,2008,41(4):1-7.
[14] Celledoni E,McLachlan R I,Owren B,et al.On conjugate B-series and their geometric structure [J].Journal of Numerical Analysis,Industrial and Applied Mathematics,2010,5(1/2):85-94.
[15] McLachlan R I,Quispel G R W,Robidoux N.Geometric integration using discrete gradients [J].Phil Trans R Soc A,1999,357(1754):1021-1045.

相似文献/References:

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备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11561018,11161017)和海南省自然科学基金(114003)资助项目.
更新日期/Last Update: 1900-01-01