Dr. Brian Moore (Department of Mathematics, UCF) will speak at this week's colloquium on time stepping with exact dissipation rates.

Abstract: Many ODE and PDE models with damping and/or exernal driving forces have properties which describe energy, mass, momentum, etc. In particular, exponential integrators, which are generalizations of Runge-Kutta, discrete gradient, and collocation methods can be constructed to preserve these properties in numerical simulations under certain restrictions. As time-stepping schemes these methods have certain advantages for particular models, because they have dissipation rates that are exact, up to machine precision. Method construction, numerical stability, and applications, resulting primarily from undergraduate research projects at UCF, will be presented.