Abstract
In this paper, the partitioned second derivative general linear methods for solving separable Hamiltonian problems are derived which are G-symplectic, interchange symmetry and have zero parasitic growth factors. Order conditions for such methods based on the theory of rooted trees are provided and examples of partitioned pairs of order 2 and 3 are given. The experiments have been performed on some separable problems and no drift in the variation of the Hamiltonian is observed in numerical experiments for long time intervals. Also, the results of numerical experiments demonstrate the efficiency of our new methods in comparison with some symplectic and G-symplectic methods.
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