Runge-Kutta methods for Hamiltonian systems in non-standard symplectic two-form

Karasozen B.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.66, pp.113-122, 1998 (SCI-Expanded) identifier identifier


Runge-Kutta methods are applied to Hamiltonian systems on Poisson manifolds with a nonstandard symplectic two-form. It has been shown that the Gauss Legendre Runge-Kutta (GLRK) methods and combination of the partitioned Runge-Rutta 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.