Symplectic Methods for Separable Hamiltonian Systems
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control
Mathematics and Computers in Simulation
Explicit symplectic partitioned Runge-Kutta-Nyström methods for non-autonomous dynamics
Applied Numerical Mathematics
Stability and consistency of discrete adjoint implicit peer methods
Journal of Computational and Applied Mathematics
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We are concerned with symplectic methods for integrating Hamiltonian systems. We focus our attention on the independent order conditions for symplectic integrators that can be expanded as P-series. This class of methods includes the important family of partitioned Runge--Kutta methods. It is known that, as in the nonpartitioned case, the conditions for a partitioned method to be symplectic act as simplifying assumptions, introducing many redundancies in the order conditions. We show that there is a one-to-one correspondence between the set of independent order conditions for symplectic partitioned methods and a suitable set of oriented graphs that we call H-trees. We count the number of such H-trees, i.e., the number of independent order conditions.