A generalized energy and QUadratic Invariant Preserving (GEQUIP) method for Hamiltonian systems with multiple invariants

It is well-known that the symplecticity and energy-conservation are the most characteristic properties of a Hamiltonian system. Meanwhile, many Hamiltonian problems allow the presence of multiple physical invariants, besides energy. This paper deals with a generalization of the EQUIP methods defined in Brugnano et al. [1], aimed at introducing additional parameters to attain further multiple invariants conservation properties, together with the symplecticity of the map. The solvability of the nonlinear system arising from the conservation requirements on multiple invariants is proved and the order of convergence on the method is discussed. Some numerical tests are reported in order to confirm the efficiency of the methods, which shows the good multiple invariants preserving property of the proposed method compared to Gauss collocation methods and EQUIP methods.