Runge-kutta methods for hamiltonian systems in non-standard symplectic two-form

Abstract

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-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

C.R. Categories:

• G.1.7