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High oscillations versus parasitic solutions

Date: 
Friday 6th July 2007 - 10:00 to 10:30
Venue: 
INI Seminar Room 1
Abstract: 

The theory of modulated Fourier expansions is a powerful tool for the study of the long-time behaviour of differential equations with highly oscillatory solutions (conservation of energy, momentum, and harmonic actions).

There is a discrete analogue that permits to study the long-time behaviour of linear multistep methods applied to (non-oscillatory) Hamiltonian systems. The parasitic solutions of the difference equations play the role of harmonic oscillations.

In this talk we explain the common ideas of both theories. This is joint-work with Christian Lubich.

Related Links

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons