Symplectic Difference Schemes for Hamiltonian Systems

Kang Feng and Mengzhao Qin ()
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Kang Feng: Institute of Computational Mathematics and Scientific/Engineering Computing
Mengzhao Qin: Institute of Computational Mathematics and Scientific/Engineering Computing

Chapter Chapter 4 in Symplectic Geometric Algorithms for Hamiltonian Systems, 2010, pp 187-211 from Springer

Abstract: Abstract The canonicity of the phase flow for time-independent Hamiltonian systems is one of the most important properties. It ensures the preservation of phase areas and the phase volume. Thus, preserving the canonicity of transition of difference schemes from one time step to the next is also important in the numerical solutions of Hamiltonian systems. The goal of this chapter is to find some simple symplectic schemes, i.e., to identify which one, among the existing difference schemes, is symplectic.

Keywords: Hamiltonian System; Symplectic Structure; Symplectic Matrix; Linear Hamiltonian System; Symplectic Matrice (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01777-3_5

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DOI: 10.1007/978-3-642-01777-3_5

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