Geometric numerical integration is an active interdisciplinary research area. The motivation for developing structure-preserving algorithms for special classes of differential equations originates from diverse areas such as astronomy, molecular dynamics, mechanics, control theory, theretical physics and numerical analysis, with important contributions form applied and pure mathematics. This seminar mainly adresses the numerical treatment of classes of ordinary differential equations by geometric integrators: symplectic methods for Hamiltonian problems, symmetric methods for reversible systems, methods preserving first integrals and numerical methods on manifolds.
Topics treated in the seminar will be:
The seminar will be organized in such a way that besides introductory lectures the participants have the possibility to work actively on theoretical and practical exercises.
E. Hairer, Ch. Lubich, G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer, Berlin, 2002, 2nd edition 2006.
A. Iserles, H.Z. Munthe-Kaas, S.P. Nørsett & A. Zanna, Lie-group methods, Acta Numerica 9, 2000, 215-365.
B. Leimkuhler, S. Reich, Simulating Hamiltonian Dynamics. Cambridge University Press, 2004.
should be sent as hard copy or by e-mail (.ps or .pdf file) to:
Prof. Dr. Gert-Martin Greuel
67663 Kaiserslautern, Germany