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arXiv:1304.0673 [math.NA]AbstractReferencesReviewsResources

On an asymptotic method for computing the modified energy for symplectic methods

Per Christian Moan, Jitse Niesen

Published 2013-04-02Version 1

We revisit an algorithm by Skeel et al. for computing the modified, or shadow, energy associated with the symplectic discretization of Hamiltonian systems. By rephrasing the algorithm as a Richardson extrapolation scheme arbitrary high order of accuracy is obtained, and provided error estimates show that it does capture the theoretical exponentially small drift associated with such discretizations. Several numerical examples illustrate the theory.

Comments: 16 pages, 7 figures
Journal: Discrete Contin. Dyn. Syst. 34 (2014) 1105-1120
Categories: math.NA
Subjects: 65P10, 37J40, 37M15
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