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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<strong>Numerical</strong> properties <strong>of</strong> the <strong>equations</strong>◮ Appropriate schemes: Gauss Runge-Kutta methodswiths∑y n+1 = y n + h b i f (Y i ),Y i = y n + hi=1s∑a ij f (Y j ),j=1b i =a ij =∫ 10∫ ci0l i (t)dt,l j (t)dt,l i (t) := ∏ i≠jt − c jc i − c j,c i = 1 2 (1 + ˜c i).◮ ˜c i are the roots <strong>of</strong> the Legendre-polynomial <strong>of</strong> degree s.Convergence order O(h 2s ).6/26 | Jonathan Seyrich (<strong>Numerical</strong> <strong>long</strong>-<strong>term</strong> <strong>integration</strong>) Tübingen | January 21, 2013
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