Construction of nearly conservative multivalue numerical methods for Hamiltonian problems

The purpose of this paper is the derivation of multivalue numerical methods for Hamiltonian problems. It is known from the literature that such methods cannot be symplectic; however, they can satisfy an alternative property, known as G-symplecticity, which still allows a long time conservation of the Hamiltonian of the dynamical system under investigation. New G-symplectic methods are derived and compared with existing ones on a selection of Hamiltonian systems.