Numerical long-term integration of geodesic equations of motion
Numerical long-term integration of geodesic equations of motion
Numerical long-term integration of geodesic equations of motion
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Problem and motivation◮ Classical explicit Runge-Kutta method in axisymmetric case:10.01h=0.01h=0.10.010.0050.0001p x01e-006-0.005∆H(t)1e-008h=1h=101e-0100.0051e-0121e-014h=0.01h=0.1h=1h=100 100000 200000 300000 400000 500000tp x0-0.00530 35 40 45 50 55 60x30 35 40 45 50 55 60 65xFigure: Energy error ∆H = | [H(yn)−H 0]/H 0 |.Figure: Poincaré sectionsEnergy conservation is important⇒ Use structure preserving integrators!4/26 | Jonathan Seyrich (<strong>Numerical</strong> <strong>long</strong>-<strong>term</strong> <strong>integration</strong>) Tübingen | January 21, 2013
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