Volume-preserving schemes and applications (Q1321708)

The authors show that when classical difference schemes such as Euler midpoint rule and fourth-order Runge-Kutta method are applied to many kinds of dynamical systems the numerical results are sometimes unsatisfactory. Then the authors point out that Euler midpoint is only volume-preserving under some strict conditions and they present an explicit volume-preserving scheme which is also structure-preserving for any dynamical systems which are source free. The authors apply these schemes, volume-preserving or not, to the system defining rigid body motion and ABC flow to see some interesting results.