Long-term control of oscillations in differential equations
Ernst Hairer and Christian Lubich
Abstract.
Ordinary differential equations arise everywhere in science -- Newton's law in physics,
N-body problems in astronomy and in molecular dynamics, engineering
problems in robotics, population models
in biology, and many more.
Since their analytic solution can be obtained only in exceptional
situations, one is usually restricted to numerical simulations and/or to
qualitative investigations of the flow. This article reviews a recent technique - the modulated
Fourier expansion - which permits to get insight into the long-term behaviour
of numerical solutions of multi-value methods as well as of analytic solutions of
highly oscillatory differential equations.
Key Words.
Modulated Fourier expansion, high oscillations.