Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 10, 14:30 ~ 15:00

It takes a wave packet to catch a wave packet

Arieh Iserles

University of Cambridge, United Kingdom   -

We are concerned with spectral methods for signals composed of wave packets, e.g. in quantum mechanics. The traditional approach is to use periodic boundary conditions, in which case standard Fourier methods are more than adequate, except that in long-term integration wave packets might reach the boundary and non-physical behaviour ensues. This motivates us to consider approximations on the entire real line. We consider and analyse in detail four candidates: Hermite polynomials, Hermite functions, stretched Chebyshev expansions and stretched Fourier expansions. In particular, we are concerned with the speed of convergence of standard and $m$-term approximations. And the winner is…

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