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Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 120))

Abstract

The aim of this work is to understand the possible role in the long-term integration of conservative systems of “G-symplectic” methods. It comes out of a collaboration with Dr Adrian Hill of the University of Bath, United Kingdom, and Dr Yousaf Habib of the National University of Science and Technology, Pakistan. Although symplectic behaviour, or the exact conservation of quadratic invariants, for irreducible methods of this type, is not possible [3], there is a G-generalization, similar to the generalization introduced by Dahlquist [6] in the study of non-linear dissipative methods. Specific issues in this research include the role of time-reversal symmetry in conservative integration, the exacerbation of parasitic effects and the construction and implementation of specific methods of increasingly high orders.

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Butcher, J.C. (2013). Dealing with Parasitic Behaviour in G-Symplectic Integrators. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-33221-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33220-3

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