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VON NEUMANN STABILITY ANALYSIS OF symplectic INTEGRATORS APPLIED TO HAMILTONIAN PDEs

Journal of Computational Mathematics 2002年第6期20卷 611-618页

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. Applied Biomathematics 100 North Country Road Setauket 美国 New York 11733

Discusses the symplectic integration of separable Hamiltonian ordinary and partial differential equations (PDE). Results of a von Neumann analysis; Spectra of linearized Hamiltonian PDEs.

关键词： symplectic integration Hamiltonian PDEs linear stability von Neumann anal- ysis.

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symplectic SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE

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Journal of Computational Mathematics 2001年第5期19卷 475-488页

作者： Xiao-wu Lu (Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA) Emory University 美国 30322

Presents a class of finite difference methods of first and second order accuracy for the computation of solutions to the quasilinear wave equations. Overview of general symplectic schemes and generating functional; Nu... 详细信息

关键词： symplectic integration Sine-Gordon equations Finite difference method.

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High-Order symplectic Schemes for Stochastic Hamiltonian Systems

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Communications in Computational Physics 2014年第6期16卷 169-200页

作者： Jian Deng Cristina Anton Yau Shu Wong Department of Mathematical and Statistical Sciences University of AlbertaEdmontonAB T6G 2G1Canada. Department of Mathematics and Statistics Grant MacEwan UniversityEdmontonAB T5J 4S2Canada.

The construction of symplectic numerical schemes for stochastic Hamiltonian systems is *** approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired *** general the proposed symplectic schemes are fully implicit,and they become computationally expensive for mean square orders greater than ***,for stochastic Hamiltonian systems preserving Hamiltonian functions,the high-order symplectic methods have simpler forms than the explicit Taylor expansion schemes.A theoretical analysis of the convergence and numerical simulations are reported for several symplectic *** numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关键词： Stochastic Hamiltonian systems symplectic integration mean-square convergence high-order schemes.

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Construction of symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

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Communications in Computational Physics 2017年第1期21卷 237-270页

作者： Peng Wang Jialin Hong Dongsheng Xu Institute of Mathematics Jilin UniversityChangchun 130012P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences100080 BeijingP.R.China University of Chinese Academy of Sciences P.R.China

We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems(SHS).Three types of systems,SHS with multiplicative noise,special separable Hamiltonians and multiple additive noise,respectively,are considered in this *** Runge-Kutta(SRK)methods for these systems are investigated,and the corresponding conditions for SRK methods to preserve the symplectic property are *** on the weak/strong order and symplectic conditions,some effective schemes are *** particular,using the algebraic computation,we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise,and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise,*** numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关键词： Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition

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symplectic orbit propagation based on Deprit’s radial intermediary

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Astrodynamics 2018年第4期2卷 375-386页

作者： Leonel Palacios Pini Gurfil Faculty of Aerospace Engineering Technion-Israel Institute of TechnologyHaifa3200003Israel

The constantly challenging requirements for orbit prediction have opened the need for better onboard propagation ***-Kutta(RK)integrators have been widely used for this purpose;however RK integrators are not symplectic,which means that RK integrators may lead to incorrect global behavior and degraded *** from Deprit’s radial intermediary,obtained by the elimination of the parallax transformation,we present the development of symplectic integrators of different orders for spacecraft orbit *** a set of numerical simulations,it is shown that these integrators are more accurate and substantially faster than Runge-Kutta-based ***,it is also shown that the proposed integrators are more accurate than analytic propagation algorithms based on Deprit’s radial intermediary solution,and even other previously-developed symplectic integrators.

关键词： symplectic integration spacecraft orbit propagation Deprit’s radial intermediary symplecticity Hamiltonian dynamics

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A symplectic ALGORITHM FOR DYNAMICS OF RIGID BODY

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Applied Mathematics and Mechanics(English Edition) 2006年第1期27卷 51-57页

作者：路英杰任革学 Department of Engineering Mechanics Communicated

For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange＇s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange＇s equations show unique advantages over the traditional Lagrange＇s equations in symplectic integrations.

关键词： rigid-body dynamics quaternion generalized momenta symplectic integration

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