ON ORDER CONDITIONS FOR PARTITIONED SYMPLECTIC METHODS

摘要

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 ill 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. [References: 9]