Geometric integration and its application (Q1012904)

Summary: Geometric integration is the general term for a set of numerical algorithms for solving differential equations that aim to reproduce qualitative features in the solution. These can be conservation laws, symmetries, symplectic structure, singularities or long time asymptotic behaviour. Often these properties are fundamental to the physical system being modelled, and to reproduce them requires more than a careful local error control. In this article I describe some of these methods, looking in particular to an application of them to solving the harmonic oscillator and to the Kepler problem in celestial mechanics, in which the advantages of them over more traditional numerical methods becomes clear.