The existence of symplectic general linear methods

We derive a criterion that any general linear method must satisfy if it is symplectic. It is shown, by considering the method over several steps, that the satisfaction of this condition leads to a reducibility in the method. Linking the symplectic criterion here to that for Runge-Kutta methods, we demonstrate that a general linear method is symplectic only if it can be reduced to a method with a single input value.