SC 98-19 Sebastian Reich: Dynamical Systems, Numerical Integration, and Exponentially
Small Estimates
Abstract: 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).
MSC: 65L05, 34C35
CR: G.1.7