8th Conference on Real Numbers and Computers

The lecture is a report on current research activities of the MuPAD group in the area of symbolic and numeric solutions of ODE (ordinary differential equations). Based on a unification of Lie-point-symmetries and Lie-Bäcklund-symmetries the results of classical Lie-symmetry approaches (for example Liouville-Arnold) to ODE are generalized thus opening new avenues for using integrability (around initial values) for wider classes of differential equations. Applications and numerical consequences of these results will be discussed and plans how to extend current solution methods, numerical as well as symbolical, to wider classes of transcendents (i.e. Painlevé transcendents) will be presented. Email address: bf@fuchssteiner.de (Benno Fuchssteiner). Real Numbers and Computers’6, 5 Nov 15-17, 2004, Dagstuhl, Germany Invited Lecture: A survey of Integer Relations algorithms and rational numbers

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