[1]张静静.基于精确数值离散的一类新的辛算法[J].江西师范大学学报(自然科学版),2015,(06):588-591.
 ZHANG Jingjing.A New Class of Symplectic Method Based on Exact Numerical Discretization[J].,2015,(06):588-591.
点击复制

基于精确数值离散的一类新的辛算法()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年06期
页码:
588-591
栏目:
出版日期:
2015-12-31

文章信息/Info

Title:
A New Class of Symplectic Method Based on Exact Numerical Discretization
作者:
张静静
河南理工大学数学与信息科学学院,河南 焦作 454000
Author(s):
ZHANG Jingjing
School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo Henan 454000,China
关键词:
精确数值离散 修正中点公式 哈密尔顿系统 辛算法
Keywords:
exact numerical discretization modified midpoint formula Hamilton system symplectic
分类号:
O 241.82
文献标志码:
A
摘要:
对数值计算中经典的中点公式参数化,基于精确数值离散的思想构造了带参数的修正中点公式.此修正中点公式是对称的具有2阶精度的辛算法,应用此修正中点公式模拟简单单摆问题.数值实验表明:对于小的初始摆角和较大的初始摆角,带参数的修正中点公式比经典的中点公式更优越.
Abstract:
The modified midpoint formula with a parameter is constructed by parameterizing the classical midpoint formula and based on the idea of exact numerical discretization.The modified midpoint formula is symmetric,second order convergent and symplectic.When applied to simple pendulum problem,it shows that the modified midpoint formula with a parameter is better than classical midpoint formula for small and large initial angular displacements.

参考文献/References:

[1] 冯康,秦孟兆.哈密尔顿系统的辛几何算法 [M].杭州:浙江科学技术出版社,2003.
[2] Hairer E,Lubich C,Wanner G.Geometric numerical integration: structure-preserving algorithms for ordinary differential equations [M].Berlin:Springer-Verlag,2006.
[3] 徐远,孔令华,王兰,等.带有阻尼项的4阶非线性薛定谔方程的显式辛格式 [J].江西师范大学学报:自然科学版,2013,37(3): 244-248.
[4] 童慧,孔令华,王兰.Dirac方程的紧致分裂多辛格式 [J].江西师范大学学报:自然科学版,2014,38(5):521-525.
[5] 王兰.多辛Preissmann格式及其应用 [J].江西师范大学学报: 自然科学版,2009,33(1),42-46.
[6] Leok M,Zhang Jingjing.Discrete Hamiltonian variational integrators [J].IMA J Numer Analy,2011,31(4):1497-1532.
[7] Marsden J E,West M.Discrete mechanics and variational integrators [J].Acta Numer,2001,10:357-514.
[8] Vladimir Dorodnitsyn,Roman Kozlov.Invariance and first integrals of continuous and discrete Hamiltonian equations[J].J Engn Math,2010,66(1/2/3): 253-270.
[9] Renfrey B Potts.Differential and difference equations [J].Amer Math Monthly,1982,89(6):402-407.
[10] Agarwal R P.Difference equations and inequalities:theory,methods and applications [M].New York:Marcel Dekker,2000.
[11] Mickens Ronald E.Nonstandard finite difference models for differential equations [M].Singapore: World Scientific,1994.
[12] Belédez A,Pascual C,Méndez D I,et al.Exact solution for the nonlinear pendulum [J].Revista Brasileira de Ensino de Fisica,2007,29(4):645-648.

备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11201125),河南省教育厅课题(12B110010)和河南理工大学博士基金(B2011-093)资助项目.
更新日期/Last Update: 1900-01-01