RUNGE-KUTTA METHODS FOR HAMILTONIAN-SYSTEMS IN NONSTANDARD SYMPLECTIC2-FORM

Runge-Kutta methods are applied to Hamiltonian systems on Poisson mani folds with a nonstandard symplectic two-form. It has been shown that t he Gauss Legendre Runge-Kutta (GLRK) methods and combination of the pa rtitioned Runge-Rutta methods of Lobatto IIIA and IIIb type are symple ctic up to the second order in terms of the step size. Numerical resul ts on Lotka-Volterra and Kermack-McKendrick epidemic disease model rev eals that the application of the symplectic Runge-Kutta methods preser ves the integral invariants of the underlying system for long-time com putations.