B. Karasozen

Runge-Kutta methods are applied to Hamiltonian systems on Poisson manifolds with a non-standard symplectic two-form. It has been shown that the Gauss Legendre Runge-Kutta (GLRK) methods and combination of the partitioned Runge-Kutta methods of Lobatto IIIA and IIIb type are symplectic up to the second order in terms of the step size. Numerical results on Lotka-Volterra and Kermack-McKendrick epidemic disease model reveals that the application of the symplectic Runge-Kutta methods preserves the integral invariants of the underlying system for long-time computations.

Keywords: Hamiltonian equations, Poisson manifolds, symplectic two-forms, symplectic Runge-Kutta methods, Lotka-Volterra equations, epidemic models