New structures in geometric numerical integration

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Many scientific phenomena in physics, astronomy, chemistry, and geoscience, are modelled by differential equations (DEs). Generally DEs have no closed form solutions, and one must rely on numerical integration. Traditionally this is done using, for example, Runge-Kutta methods or linear multistep methods, respectively finite difference or finite element methods. Recently, however, novel so-called ‘geometric’ integration methods that preserve qualitative features of many DEs exactly (as opposed to traditional methods) have been discovered, leading to crucial stability improvements. Combining aspects of dynamical systems theory and traditional numerical DEs, this project will improve, extend, and systematise this new field of geometric integration.