MS28 ~ Monday, May 22, 1995 ~ 7:30 PM

Numerical Trajectories

Computer modeling of nonlinear systems is a subject of great importance in scientific investigation. Nonlinear dynamical models often contain trajectories that exhibit sensitive dependence on initial conditions. It follows that moderate- to long-time computer simulations of these trajectories are problematic, because of the resulting amplification of discretization errors. The speakers in this minisymposium will focus on a critical question: Is the computer-generated trajectory close to a true trajectory of the system? This is the so-called "shadowing" question. In some cases, the answer hinges on the level and uniformity of hyperbolicity present in the system.

Organizer: Timothy Sauer, George Mason University

Numerical Shadowing Near Hyperbolic Trajectories
Erik S. Van Vleck, Colorado School of Mines
On the Numerical Solution of the Sine-Gordon Equation
Constance Schober, University of Colorado, Boulder
Bi-Shadowing in Semi-Hyperbolic Systems
Alexei Pokrovski, University of Queensland, Australia
Obstructions to Shadowing When a Lyapunov Exponent Fluctuates About Zero
Timothy Sauer, Organizer