State-dependent symplecticity and area preserving numerical methods

摘要

We introduce the definition of state-dependent symplecticity as a useful tool of investigation to discover nearby symplecticity in symmetric non-symplectic one-step methods applied to two-dimensional Hamiltonian systems. We first relate this property to Poisson systems and to the trapezoidal method, and then investigate Runge-Kutta and discrete gradient symmetric methods. (c) 2006 Elsevier B.V. All rights reserved.