Symplectic explicit Runge-Kutta Nyström methods
by
Lin-Yi Chou
Department of Mathematics, University of Auckland
Coauthors: Philip W. Sharp (University of Auckland)

Unlike symplectic Runge-Kutta methods which are necessarily implicit, symplectic Runge-Kutta Nyström (ERKN) can be explicit provided the Hamilton for the problem being solved has the correct form. Fortunately, the Hamilton for a number of practical problems has this form and hence symplectic ERKN methods have an important role to play in the numerical solution of Hamilton problems.

We present new symplectic explicit Runge-Kutta Nyström methods of orders four and five and compare their performance with existing methods.

Date received: August 27, 1999