VON NEUMANN STABILITY ANALYSIS OF SYMPLECTIC INTEGRATORS APPLIED TO HAMILTONIAN PDEs
VON NEUMANN STABILITY ANALYSIS OF SYMPLECTIC INTEGRATORS APPLIED TO HAMILTONIAN PDEs
摘要
Discusses the symplectic integration of separable Hamiltonian ordinary and partial differential equations (PDE). Results of a von Neumann analysis; Spectra of linearized Hamiltonian PDEs.
Discusses the symplectic integration of separable Hamiltonian ordinary and partial differential equations (PDE). Results of a von Neumann analysis; Spectra of linearized Hamiltonian PDEs.
作者
Helen M. Regan (Applied Biomathematics 100 North Country Road, Setauket, New York 11733, USA)Current address: National Center for Ecological Analysis and Synthesis, University of California Santa Barbara, 735 State St., Suite 300, Santa Barbara, CA 93101, USA. Email: regan@nceas.ucsb.edu, Phone: (805) 892 2522, Fax: (805) 892 2510.
参考文献9
-
1Robert McLachlan.Symplectic integration of Hamiltonian wave equations[J].Numerische Mathematik.1993(1)
-
2Qin Meng-Zhao,Zhu Wen-Jie.Construction of higher order symplectic schemes by composition[J].Computing (-).1992(3-4)
-
3P.J. Olver.Applications of Lie groups to differential equations[]..1993
-
4B.M. Herbst and M.J. Ablowitz.Numerical homoclinic instabilities in the sine-Gordon equation[]..1992
-
5V.I. Arnold.Mathematical methods of classical mechanics[]..1989
-
6E. Hairer,S.P. Nφrsett,and G. Wanner.Solving ordinary differential equations I: Nonstiff problems[]..1993
-
7D. Okunbor.Canonical methods for Hamiltonian systems: numerical experiments[]..1992
-
8J.M. Sanz-Serna and M.P. Calvo,Numerical Hamiltonian problems. Chapman and Hall . 1994
-
9R.I. McLachlan and P. Atela.The accuracy of symplectic integrators[]..1992
-
1张然,刘宏宇,张凯.Numerical Dispersion Relation of Multi-symplectic Runge-Kutta Methods for Hamiltonian PDEs[J].Northeastern Mathematical Journal,2006,22(3):349-356.
-
2Wei Sun Xin Wu Guo-Qing Huang.Symplectic integrators with potential derivatives to third order[J].Research in Astronomy and Astrophysics,2011,11(3):353-368. 被引量:2
-
3Hai ZHANG,Wei JIANG.Asymptotic Stability Criteria for Singular Differential Nonlinear Systems with Time-Varying Delays[J].Journal of Mathematical Research and Exposition,2010,30(4):664-674.
-
4Zhongsheng WANG Zhigang ZENG Xiaoxin LIAODepartment of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan Hubei 430074, P. R. China.STABILITY CRITERIA FOR A CLASS OF UNCERTAIN SYSTEMS WITH TIME-DELAY[J].Systems Science and Systems Engineering,2003,12(2):204-209. 被引量:2
-
5Ling-shu Wang,Ying Wang.Preservation of Equilibria for Symplectic Methods Applied to Hamiltonian Systems[J].Acta Mathematicae Applicatae Sinica,2010,26(2):219-228. 被引量:1
-
6KOU,Chun-hai(寇春海),ZHANG,Shu-nian(张书年).STABILITY CRITERIA IN TERMS OF TWO MEASURES FOR DELAY DIFFERENTIAL EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2002,23(3):311-320.
-
7CHEN ZHENG-XIN CHEN QIONG.Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability[J].Communications in Mathematical Research,2012,28(1):26-42. 被引量:1
-
8Guosheng Yu (School of Math. and Statistics,Huazhong University of Science and Technology,Wuhan 430074,College of Math. and Computer Science,Jianghan University,Wuhan 430056,Hubei).EXPONENTIAL STABILITY CRITERIA FOR STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS[J].Annals of Differential Equations,2009,25(3):363-370.
-
9PeterGrtz.BACKWARD ERROR ANALYSIS OF SYMPLECTIC INTEGRATORS FOR LINEAR SEPARABLE HAMILTONIAN SYSTEMS[J].Journal of Computational Mathematics,2002,20(5):449-460. 被引量:5
-
10Yang LI,Wende LIU.Maximal Graded Subalgebras of the General Linear Lie Superalgebras over Superrings[J].Journal of Mathematical Research with Applications,2015,35(2):149-156. 被引量:1