Dipartimento Interuniversitario di Matematica            

Geometric integration is a new branch of numerical analysis which aims to the development of numerical methods which incorporate qualitative information of the underlying problem into their structure.
In the last years, the numerical analysis of differential equations has changed significantly. Previously, the main efforts of algorithm developers were aimed at developing robust 'black box' integrators, whose main goal was to obtain fast solvers with small global error. Recently, it has been increasingly clear that for many applications it is crucial to preserve qualitative features of the underlying continuous equations in the numerical solution. Examples are preservation of energy, momentum or symplectic structures, and numerical solutions that evolve on a given manifold. During the last decade, we have seen the development of several different new algorithms, many inspired by geometrical ideas. In the same period, the commonly used programming languages in computational science have shifted from concrete languages such as FORTRAN and C towards modern object oriented languages such as C++ and MATLAB5. This development allows us to capture advanced mathematical concepts as objects in a computer program, and might further boost the interest in applying geometrical concepts in computational mathematics.

Last update 3 December 2001