[1]曾文平,孔令华.辛算法的发展历史与现状[J].华侨大学学报(自然科学版),2004,25(2):113-117.[doi:10.3969/j.issn.1000-5013.2004.02.001]
 Zeng Wenping,Kong Linghua.History and Present State of Symplectic Algorithm[J].Journal of Huaqiao University(Natural Science),2004,25(2):113-117.[doi:10.3969/j.issn.1000-5013.2004.02.001]
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辛算法的发展历史与现状()
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《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第25卷
期数:
2004年第2期
页码:
113-117
栏目:
出版日期:
2004-04-20

文章信息/Info

Title:
History and Present State of Symplectic Algorithm
文章编号:
1000-5013(2004)02-0113-05
作者:
曾文平孔令华
华侨大学数学系; 华侨大学数学系 福建泉州362011; 福建泉州362011
Author(s):
Zeng Wenping Kong Linghua
Dept. of Math., Huaqiao Univ., 362011, Quanzhou, China
关键词:
Hamilton系统 辛算法 进展研究
Keywords:
Hamilton system symplectic algorithm a study on the advances
分类号:
O241.821
DOI:
10.3969/j.issn.1000-5013.2004.02.001
文献标志码:
A
摘要:
Hamilton系统是用来描述无耗散的物理过程与物理现象的一种力学系统 .辛几何算法是保结构算法中的一种,国内外学者在这一领域的研究,取得了丰硕的成果 文中介绍针对Hamilton系统的辛几何算法发展的简要历史、研究现状和未来发展与应用,尤其是国内学者在这一领域的主要工作 .
Abstract:
Hamilton system is a mechanical system for the use of describing non-dissipative physical process and physical phenomenon. The algorithm of symplectic geometry is one of structure preserving algorithms. Scholars at home and abroad have scored great successes in this field. Aiming at algorithm of symplectic geometry for Hamilton system, the authors describe its concise history, present state, prospect and applications, especially the primcipal works of Chinese scholars in this field.

参考文献/References:

[1] Vogelaere R De. Method of integration which preserve the contact transformation property of the Hamilton equations [J]. Notre Dame Ind, 1956(4):98-154.
[2] Ruth R D. A canonical integration technique [J]. IEEE Transactions on Nuclear Science, 1983(3):2669-2671.
[3] Feng Kang. On difference schemes and symplectic geometry [A]. 北京:科学出版社, 1985.42-58.
[4] Feng Kang. Difference schemes for Hamiltonian formalism and symplectic geometry [J]. Journal of Computational Mathematics, 1986(3):279-289.
[5] Feng Kang. How to compute property Newton’s equation of motion [A]. Tianjin:Nakai Univ.Press, 1986.12-22.
[6] FENG K, Wu H M, Qin M Z. Construction fo canonical difference schemes for Hamilton formalism via generating functions [J]. Journal of Computational Mathematics, 1989.71-96.
[7] Zhong Ge, Feng Kang. On the approximation for linear Hamiltonian system [J]. Journal of Computational Mathematics, 1988(1):88-97.
[8] 冯康, 秦孟兆. Hamilton力学体系的Hamilton算法 [J]. 自然科学进展-国家重点实验室通讯, 1990(2):110-120.
[9] 冯康. 冯康文集(Ⅱ) [M]. 北京:国防工业出版社, 1995.12-103.
[10] Qin Mengzhao. A difference scheme for the Hamiltonian equation [J]. Journal of Computational Mathematics, 1987(3):203-209.
[11] QIN M Z, Zhang M Q. Multi-stage symplectic schemes of two kinds of Hamiltonian systems for wave equations [J]. Computers & Mathematics with Applications, 1990(4):51-62.
[12] 秦孟兆. 辛几何及计算哈密顿力学 [J]. 力学与实践, 1996(6):1-20.
[13] Lasagni F M. Canonical Runge-Kutta methods [J]. Zeitschrift für angewandte Mathematik und Physik, 1933(5):952-953.
[14] Sanz-Serna J M. Runge-Kutta schemes for Hamilton systems [J]. Bit Numerical Mathematics, 1988.877-883.doi:10.1007/BF01954907.
[15] Suris Y B. The canonicity of mappings generated by Runge-Kutta type method when integrating the systems [J]. Zh Vychist Mat Fiz, 1989.202-211.
[16] Sun Geng. Construction of high order symplectic Runge-Kutta methods [J]. Journal of Computational Mathematics, 1993(3):250-260.
[17] Sun Geng. Symplectic PRK methods [J]. Journal of Computational Mathematics, 1993(4):365-372.
[18] Tang Yifa. The symplecticity of multi-step methods [J]. Computers & Mathematics with Applications, 1993(1):83-90.
[19] Hairer E, Leone P. Order barriers for symplectic multi-step methods [J]. Numerical Analysis, 1997(2):53-85.
[20] 蒋长锦. 四级四阶对角隐式辛Runge-Kutta方法参数计算 [J]. 数值计算与计算机应用, 2002(3):161-166.doi:10.3969/j.issn.1000-3266.2002.03.001.
[21] Bridges T J. Multisymplectic structure, Boussinesq equation and periodic traveling waves [A]. Singapore:World Scientific, 1995.135-217.
[22] Bridges T J. A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities [M]. New York: Pineridge Press, 1993.331-357.
[23] Bridges T J. Multisymplectic structures and wave propagation [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1997.147-190.doi:10.1017/S0305004196001429.
[24] Bridges T J, Reich S. Multisymplectic integrators: Numerical schemes for Hamilon PDEs that conserve symplecticity [J]. Physics Letters, 2001.184-193.
[25] Reich S. Finite volume method for multisymplecitc PDEs [J]. BIT Numerical Mathematics, 2000(3):559-582.
[26] Bridges T J, Reich S. Multisymplectic spectral discretization for the Z-K and shallow water equation [J]. Physica, 2001.491-504.
[27] Marsden J E, Patric G P, Shkoller S. Multisymplectic geometry, variational integrators, and nonlinear PDEs [J]. Communications in Mathematical Physics, 1998(4):351-395.
[28] Hong J L, Liu Y. Multisymplecticity of the center box discret for a class of Hamilton PDEs and an application to quasi-periodic solitary wave of dqpkdv equation [J]. Preprint, 2004.
[29] Hong J L, Qin M Z. Multisymplectic of center box discretization of Hamilton PDEs with m2 space dimensions [J]. Applied Mathematics Letters, 2002, (8):1005-1011.doi:10.1016/S0893-9659(02)00077-0.
[30] Hong J L, Lin Y. Hans Munthe-Kass, Antonella Zanna, Globality conservative properties and error estimation of a multisympletic scheme for schrodinger with variable coefficients [J]. Applied Mathematics Letters, 2004.
[31] QIN M Z, Wang Y S. Multi-symplectic schemes for nonlinear wave equation [J]. Collected Works of CCAST-WL, 2001.69-86.
[32] 秦孟兆. 多辛几何差分格式 [A]. 北京:高等科学技术中心出版社, 2000.17-22.
[33] Chen J B, Qin M Z, Tang Y F. Symplectic and multi-symplectic methods for the Schrodinger equation [J]. Computers and Mathematics with Applications, 2002.1032-1123.
[34] Chen J B, Qin M Z. Miltisymplectic fourier pseudospectral method for the NLSE [J]. Numerical Analysis, 2001.503-512.
[35] 王雨顺, 秦孟兆. 变分与无限维系统的高精度辛格式 [J]. 计算数学, 2002(4):431-436.doi:10.3321/j.issn:0254-7791.2002.04.005.
[36] QIN M Z, Zhu W J. Volume-preserving schemes and numerical experiments [J]. Computers & Mathematics with Applications, 1993(4):33-42.
[37] 秦孟兆. 波动方程的两种哈密顿型蛙跳格式 [J]. 计算数学, 1988(3):272-281.
[38] 秦孟兆. 任意阶精度蛙跳格式稳定性分析 [J]. 计算数学, 1992(1):1-9.
[39] QIN M Z, Zhu W J. Construction of symplectic schemes for wave equations via Hyperbolic functions sinh(x), cosh(x) and tanh(x) [J]. Computers & Mathematics with Applications, 1993(8):1-11.
[40] 蒋长锦. 有限区间上多辛Preissmann格式及其附加条件 [J]. 中国科学技术大学学报, 2002(4):403-411.doi:10.3969/j.issn.0253-2778.2002.04.004.
[41] 曾文平. 高阶Schrodinger方程的哈密尔顿型蛙跳格式 [J]. 高等学校计算数学学报, 1995(4):305-317.
[42] 曾文平. 用Hyperbolic函数构造 Schrodinger方程的辛格式 [J]. 应用数学学报, 1996(3):424-430.
[43] 曾文平. 用Hyperbolic函数构造高阶Schrodinger方程的辛格式 [J]. 华侨大学学报(自然科学版), 1998(1):6-11.
[44] Zeng Wenping. A leap frog finite difference scheme for a class of nonlinear schrodinger equation of high order [J]. Journal of Computational Mathematics, 1999(2):133-138.
[45] 曾文平, 黄浪扬, 秦孟兆. "good Bousinesque"方程的多辛算法 [J]. 应用数学和力学, 2002(7):744-747.
[46] 黄浪扬. 四阶杆振动方程的tanh(x)辛格式 [J]. 华侨大学学报(自然科学版), 2002(3):217-221.doi:10.3969/j.issn.1000-5013.2002.03.001.
[47] Huang Langyang, Zeng Wenping, Qin Mengzhao. Construct of multisymplectic scheme for"good Bousinesque"equation [J]. Journal of Computational Mathematics, 2003(6):702-715.
[48] 曾文平. 用Hyperbolic函数构造四阶杆振动方程的显式辛格式 [A]. 西安:陕西人民教育出版社, 2003.45-50.
[49] 孔令华, 曾文平. 四阶杆振动方程的多级辛格式 [J]. 贵州大学学报(自然科学版), 2003(3):247-251.doi:10.3969/j.issn.1000-5269.2003.03.005.
[50] 黄浪扬. 四阶杆振动方程的sinh(x)蛙跳辛格式 [J]. 华侨大学学报(自然科学版), 2003(2):125-130.doi:10.3969/j.issn.1000-5013.2003.02.003.
[51] 黄浪扬. 四阶杆振动方程的cosh(x)显式辛格式 [J]. 华侨大学学报(自然科学版), 2003(3):239-244.doi:10.3969/j.issn.1000-5013.2003.03.003.
[52] 曾文平, 孔令华. 四阶杆振动方程的一族高稳定的十字架格式 [J]. 数学研究, 2003(3):288-292.doi:10.3969/j.issn.1006-6837.2003.03.011.
[53] 曾文平, 郑小红. 四阶杆振动方程的多辛格式 [J]. 漳州师范学院学报(自然科学版), 2003(4):1-5.doi:10.3969/j.issn.1008-7826.2003.04.001.
[54] 曾文平. Schrǒdinger方程的高精度辛格式 [J]. 厦门大学学报(自然科学版), 2003(6):697-700.doi:10.3321/j.issn:0438-0479.2003.06.004.

备注/Memo

备注/Memo:
国务院侨务办公室科研基金资助项目(02QZR07)
更新日期/Last Update: 2014-03-23