Numerical and Computational Challenges
in Science and Engineering Program
LECTURE
Friday, October 19, 2001, 3:00 pm, room 230
Harbir Lamba
Department of Mathematical Sciences, George Mason University
(Visiting the Fields Institute)
Adaptive Timestepping Algorithms and (other) Discontinuous Dynamical
Systems
I will begin with a brief description of adaptive timestepping algorithms
for ODEs based upon embedded Runge-Kutta pairs and then present two
results. The first is a shadowing result for such algorithms close to
hyperbolic equilibria while the second concerns the observed stability
of such algorithms when applied to dissipative ODEs.
Time permitting, I will then describe classes of problems from electrical
engineering and economics that include hysteresis effects (such as the
hysteresis displayed by magnetic materials). These result in systems
of ODEs with unusual discontinuities and history dependence and present
some interesting theoretical and numerical questions.
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