Computational Astrophysics
Wilhelm Kley
Universität Tübingen
Chapter Overview (preliminary)
The script for the individual lectures will be found in ILIAS.
1. Errors in numerical computations
2. Two-Body problem / root finding
- Kepler's equation
- Newton-method
- Fixpoint-Iteration
Literatur:
Murray, C.D. & Dermott, S.F.: Solar System Dynamics, Chap. 2.
5. Nonlinear Systems
- Logistic map
- Lyapunov Exponent
- driven physical pendulum
- Poincare sections
Literatur:
- Baker, G.L. & Gollub, J.P.: Chaotic Dynamics
- Schuster, H.-G.: Deterministic Chaos
6. N-body / ordinary differential equations (ODEs)
- Numerical integration of the two-body problem
- Runge-Kutta methods
- Euler, Heun, RK4 methods
- Adaptive integration
- Stability of integration methods
7. Symplectic integrators
- Example: Leapfrog / Verlet
- Symplectic map
- Hamilton's equations
- discrete symplectic time evolution
(examples: Explicit Euler, partitioned Euler)
- methods of higher order
(examples: Euler-Cromer, Verlet)
- equivalent Hamiltonian
(Baker-Campbell-Hausdorff formula)
Literature:
- Thijssen, J.M.: Computational Physics, Kap.8
- Kinoshita, H. et al.Symplectic Integrators and their application to dynamical astronomy
in Celestial Mechanics and Dynamical Astronomy, Vol.50, 59-71 (1990)
- Yoshida, H.Construction of higher order symplectic integrators
in Physics Letters A, Vol.150, 261-268 (1990)
8. Asteroid orbits in the Solar System
9. Stellar structure and stability
- Lane Emden equation
- 1D hydrodynamics
- Upwind method
- solution of spherically sym. equations
- oscillations of polytropic stars
- stability of polytropic stars