January 20, 2019

Numerical and Computational Challenges in Science and Engineering Program

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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