Speaker: Dave Williams, Applied Mathematics
Title:
Date: Thursday, May 22, 2003
Time: 2:30 - 3:20pm
Place: Guggenheim Room AMATH Library
Abstract. I will discuss the Method of Amplitude Equations (formerly Renormalization) in the context of solving Weakly-Nonlinear ODEs. Regular perturbations fail to approximate the solutions of many weakly-nonlinear problems over long timescales. One approach to this difficulty is to introduce multiple time scales and use the added degrees of freedom to eliminate so-called secular terms. This approach works well for a wide variety of problems but can be improved in some cases, particularly when the "appropriate" time scales are not immediately evident. The Method of Amplitude Equations uses near-identity transformations to eliminate secular terms (similar to Averaging) and can be repeatedly applied to give approximations on even longer timescales. It is also likely that this method (in a slightly more general form) can be used to solve a wider variety of problems, such as those BVPs where we would ordinarily use Matched Asymptotics.
Everyone welcome!