Abstract:
This thesis investigates numerical methods for long-term integration of Hamiltonian systems. Hamiltonian systems play an important role in countless applications in physics and biology. In the two introductory chapters Hamiltonian systems are analysed and suitable integrators of Runge{Kutta type are identified. We find competitive explicit methods for separable Hamiltonians and implicit methods of arbitrary high order for general Hamiltonians. In the remain of the thesis the specific features of the proposed integrators are examined. Rigorous numerical testing verifies the theoretical performance and shows their superiority to standard integrators. Another emphasis lies on implementational issues such as iteration methods, predictors and variable step size. Additionally we numerically investigate the effects of switching the order of the integrator.