The authors investigate the numerical solution of a Hamiltonian system, especially the property called“symplecticness” of a numerical method which consists in the preservation of some differential 2-form. First F. M. Lasagni [Integration methods for Hamiltonian differential equations. (Unpublished manuscript)] has studied this property of multi- derivative () Runge-Kutta methods. The main results of this paper are:
1) It is shown that an irreducible Runge-Kutta method can be symplectic only for , i.e., for standard Runge-Kutta methods.
2) It is shown that in this case the conditions of Lasagni for symplecticness are also necessary, so there are no symplectic multi- derivative Runge-Kutta methods.