Almost Symplectic Runge-Kutta Schemes for Hamiltonian Systems

Abstract

Symplectic Runge-Kutta schemes for integration of general Hamiltonian systems are implicit. In practice, the implicit equations are often approximately solved based on the Contraction Mapping Principle, in which case the resulting integration scheme is no longer symplectic. In this paper, the authors prove that, under suitable conditions, the integration scheme based on an n-step successive approximation is Omicron(Delta(exp n+2) away from a symplectic scheme with Delta epsilon (0,1). Therefore, this scheme is "almost" symplectic when n is large.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2002
Accession Number
ADA438924

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  • Xiaobo Tan

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  • University of Maryland

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  • C4I

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  • Abstracts
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