MS14 ~ Sunday, May 21, 1995 ~ 7:30 PM

Numerical Integration of Hamiltonian Dynamical Systems by Conserving Algorithms

It is natural to seek integration algorithms for dynamical systems that preserve as much as possible of the underlying structure. This allows meaningful interpretation of some aspects of the computed data for times far longer than those predicted by error bounds alone. It can also lead to improved error propagation features. Furthermore, conserved quantities are usually crucial for physical reasons and loss of conservation can make computations meaningless.

For Hamiltonian dynamical systems two important structural properties are: (i) conservation of integrals, such as the Hamiltonian, in autonomous problems, and (ii) conservation of the symplectic form. For non-integrable systems it is not possible to find numerical methods that inherit both of these properties. In recent years much attention has been devoted to symplectic algorithms. In this minisymposium, the speakers will discuss other types of conservative algorithms. In particular conservation of the Hamiltonian and of linear and angular momentum will play an important role in the algorithms discussed.

Organizers: John Maddocks, University of Maryland, College Park and Andrew Stuart, Stanford University

The Rate of Error Growth of Hamiltonian Conserving Integrators
Andrew Stuart, Organizer; and D.J. Estep, Georgia Institute of Technology
Recent Results on the Numerical Integration of Nonlinear Hamiltonian Systems with Symmetry
Oscar Gonzalez, Stanford University
Conservative Schemes for Hamiltonian Systems
Jian-Ming Xu, Rutgers University; and John Maddocks, Organizer
Unconstrained Hamiltonian Formulations of Constrained Lagrangian Dynamics
John Maddocks, Organizer; D.J. Dichmann and R.L. Pego, University of Maryland, College Park; and Jian-Ming Xu, Rutgers University