A G-symplectic method with order 6

Abstract

G-symplectic methods are an alternative to symplectic Runge–Kutta in that they have similar numerical behaviour but are less expensive computationally. In this paper, a new method is derived which is symmetric, G-symplectic, has zero parasitic growth factors and has order 6. Although there are five stages, two of these are explicit and the remaining three are diagonally implicit. The method is multivalue, with four quantities passed from step to step. No drift in the variation of the Hamiltonian is observed in numerical experiments for long time intervals if the stepsize is sufficiently small.