VOLUME-PRESERVING ALGORITHMS FOR SOURCE-FREE DYNAMICAL-SYSTEMS

In this paper, we first expound why the volume-preserving algorithms a re proper for numerically solving source-free systems and then prove a ll the conventional methods are not volume-preserving. Secondly, we gi ve a general method of constructing volume-preserving difference schem es for source-free systems on the basis of decomposing a source-free v ector field as a finite sum of essentially 2-dimensional Hamiltonian f ields and of composing the corresponding essentially symplectic scheme s into a volume-preserving one. Lastly, we make some special discussio ns for so-called separable source-free systems for which arbitrarily h igh order explicit revertible volume-preserving schemes can be constru cted.