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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

High oscillations versus parasitic solutions

Author: Hairer Ernst (University of Geneva)

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.

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