I am wondering, if anybody knows some paper, that study convergence and stability of Partitioned RungKutta Methods (especially Lobatto IIIAB) applied on separable Hamiltonian system.
Google says: Partitioned RungeKutta Methods for Separable Hamiltonian Problems by L Abia  1993  Cited by 30  Related articles PARTITIONED RUNGEKUTTA METHODS. 619. Hamiltonian problems if, for all Hamiltonian functions H in this class, and at each point (po, qo) in the domain of ... www.jstor.org/stable/2153105 

