Structure Preserving Schemes for Birkhoff 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 15 in Symplectic Geometric Algorithms for Hamiltonian Systems, 2010, pp 617-639 from Springer

Abstract: Abstract A universal symplectic structure for a Newtonian system including nonconservative cases can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics. In this chapter, the symplectic geometry structure of Birkhoffian system is discussed, and the symplecticity of Birkhoffian phase flow is presented. Based on these properties, a way to construct symplectic schemes for Birkhoffian systems by the generating function method is explained[SSQS07],[SQ03].

Keywords: Hamiltonian System; Lagrangian Submanifold; Error Comparison; Symplectic Mapping; Double Logarithmic Scale (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_16

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DOI: 10.1007/978-3-642-01777-3_16

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