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I am wondering, if anybody knows some paper, that study convergence and stability of Partitioned Rung-Kutta Methods (especially Lobatto IIIAB) applied on separable Hamiltonian system.

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Google says:

  • L. Abia and J. M. Sanz-Serna, Partitioned Runge-Kutta Methods for Separable Hamiltonian Problems, Mathematics of Computation Vol. 60, No. 202 (Apr., 1993), pp. 617-634, doi:10.2307/2153105.
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The paper

  • R. I. McLachlan, Y. Sun, and P. S. P. Tse, Linear Stability of Partitioned Runge–Kutta Methods, SIAM Journal on Numerical Analysis Vol. 49, Iss. 1 (2011) 232-263, doi:10.1137/100787234

addresses explicitly linear separable Hamiltonian ODEs and re-uses some results from the older paper

  • Laurent O. Jay and Linda R. Petzold, Highly Oscillatory Systems and Periodic-Stability, Preprint 95-015, Army High Performance Computing Research Center, Stanford, CA, 1995, ResearchGate.
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