A symmetric nearly preserving general linear method for Hamiltonian problems

This paper is concerned with the numerical solution of Hamiltonian problems, by means of nearly conservative multivalue numerical methods. In particular, the method we propose is symmetric, G-symplectic, diagonally implicit and generates bounded parasitic components over suitable time intervals. Numerical experiments on a selection of separable Hamiltonian problems are reported, also based on real data provided by Nasa Horizons System.