TY - THES A1 - Reich, Sebastian T1 - Dynamical Systems, Numerical Integration, and Exponentially Small Estimates N2 - Dynamical systems with two well-separated time-scales are investigated using normal form theory. Exponential estimates for the normal form truncation error are derived and applied to the numerical integration of differential equations (backward error analysis) and the reduction of highly oscillatory Hamiltonian systems (constrained dynamics and correcting potentials). The theoretical results are used to formulate new algorithms for the time integration of conservative Hamiltonian systems (projected multiple time stepping, soft constraints, rigid bodies, symplectic variable step-size methods). T3 - ZIB-Report - SC-98-19 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3622 ER -